Documentation Verification Report

Basic

📁 Source: Mathlib/Computability/Primrec/Basic.lean

Statistics

MetricCount
Definitionsunpaired, Primcodable, bool, empty, fin, ofDenumerable, ofEquiv, option, prod, subtype, sum, toEncodable, ulower, unit, PrimrecBounded, PrimrecPred, PrimrecRel, Primrec₂
18
Theoremsadd, casesOn', casesOn1, const, id, mul, of_eq, pow, prec1, pred, sub, swap, swap', mem_range_encode, prim, and, beq, bind_decode_iff, comp, comp₂, cond, const, decode, decode₂, dom_bool, dom_bool₂, dom_denumerable, dom_finite, dom_fintype, encdec, encode, encode_iff, eq, fin_succ, fin_val, fin_val_iff, fst, id, ite, list_findIdx₁, list_getElem?₁, list_idxOf₁, map_decode_iff, nat_add, nat_bodd, nat_casesOn, nat_casesOn', nat_casesOn₁, nat_div, nat_div2, nat_double, nat_double_succ, nat_findGreatest, nat_iff, nat_iterate, nat_le, nat_lt, nat_max, nat_min, nat_mod, nat_mul, nat_rec, nat_rec', nat_rec₁, nat_sub, not, ofNat, ofNat_iff, of_eq, of_equiv, of_equiv_iff, of_equiv_symm, of_equiv_symm_iff, of_graph, option_bind, option_bind₁, option_casesOn, option_get, option_getD, option_getD_default, option_guard, option_iget, option_isSome, option_map, option_map₁, option_orElse, option_some, option_some_iff, or, pair, pred, primrecPred, snd, subtype_mk, subtype_val, subtype_val_iff, succ, sumCasesOn, sumInl, sumInr, to₂, ulower_down, ulower_up, unpair, and, comp, decide, not, of_eq, or, primrecRel, comp, comp₂, decide, not, of_eq, swap, comp, comp₂, const, curry, encode_iff, left, mk, natPair, nat_iff, nat_iff', ofNat_iff, of_eq, option_some_iff, pair, primrecRel, right, swap, uncurry, unpaired, unpaired', primrecPred_iff_primrec_decide, primrecRel_iff_primrec_decide
139
Total157

Nat

Definitions

NameCategoryTheorems
unpaired 📖CompOp
12 mathmath: Primrec.pow, Primrec₂.unpaired, Primrec.add, Primrec₂.unpaired', Partrec.rfind', Partrec₂.unpaired', Primrec.sub, Primrec.mul, Partrec₂.unpaired, Primrec.swap, Primrec.casesOn', Primrec₂.nat_iff

Nat.Primrec

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalNat.unpairedof_eq
id
Nat.unpair_pair
add_zero
casesOn' 📖mathematicalNat.unpaired
Nat.pair
of_eq
Nat.unpair_pair
casesOn1 📖of_eq
prec1
Nat.unpair_pair
const 📖
id 📖of_eq
Nat.pair_unpair
mul 📖mathematicalNat.unpairedof_eq
add
Nat.unpair_pair
MulZeroClass.mul_zero
add_comm
of_eq 📖
pow 📖mathematicalNat.unpaired
Monoid.toNatPow
Nat.instMonoid
of_eq
const
mul
Nat.unpair_pair
pow_zero
prec1 📖mathematicalNat.pairof_eq
const
id
Nat.unpair_pair
pred 📖of_eq
id
Nat.instCanonicallyOrderedAdd
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
sub 📖mathematicalNat.unpairedof_eq
id
pred
Nat.unpair_pair
tsub_zero
Nat.instOrderedSub
swap 📖mathematicalNat.unpaired
Function.swap
Nat.pair
of_eq
swap' 📖mathematicalNat.unpairedFunction.swapof_eq
swap
Nat.unpair_pair

Primcodable

Definitions

NameCategoryTheorems
bool 📖CompOp
16 mathmath: ComputablePred.decide, Primrec.dom_bool, Primrec.and, computablePred_iff_computable_decide, Primrec.beq, Primrec.option_isSome, Primrec.dom_bool₂, primrecPred_iff_primrec_decide, primrecRel_iff_primrec_decide, PrimrecPred.decide, Primrec.or, Primrec.not, ComputablePred.computable_iff, PrimrecRel.decide, Computable.nat_bodd, Primrec.nat_bodd
empty 📖CompOp
fin 📖CompOp
9 mathmath: Primrec.fin_val, Primrec.fin_succ, Primrec.vector_get, Primrec.fin_val_iff, Primrec.fin_curry, Computable.vector_get, Primrec.fin_curry₁, Primrec.fin_app, Computable.fin_app
ofDenumerable 📖CompOp
112 mathmath: Nat.Partrec.Code.encode_lt_comp, Primrec.nat_double, Computable.encode_iff, Computable.list_getElem?, Primrec.nat_add, Computable.encode, Nat.Partrec.Code.primrec_pappAck_step, not_primrec_ack_self, Primrec.list_length, Primrec.list_findIdx₁, Nat.Partrec'.to_part, Primrec.list_getElem?₁, Computable.ofNat, Primrec₂.unpaired, Nat.Partrec.Code.primrec_pappAck, not_primrec₂_ack, Computable.decode, Nat.Partrec.Code.primrec₂_comp, Nat.Partrec.Code.instCountableSubtypePFunPartrec, ComputablePred.rice₂, Primrec.list_idxOf, Nat.Partrec.Code.encodeCode_eq, Primrec₂.encode_iff, Computable.bind_decode_iff, Primrec.nat_lt, Primrec₂.unpaired', Computable.map_decode_iff, ManyOneDegree.liftOn₂_eq, Nat.Primrec'.prim_iff₂, Primrec.nat_mul, Nat.Partrec.Code.instCountableSubtypeForallComputable, Nat.Primrec'.prim_iff, ComputablePred.halting_problem_not_re, ManyOneDegree.liftOn_eq, manyOneReducible_toNat_toNat, Partrec₂.unpaired', Nat.Partrec.Code.primrec_evaln, Primrec.nat_le, Nat.Partrec.Code.primrec_rfind', Computable.nat_strong_rec, Primrec.fin_val, Primrec.decode₂, Nat.Partrec.Code.primrec₂_pair, Partrec.nat_iff, Primrec.unpair, Primrec.list_range, Computable.eqv, Computable.unpair, Primrec.nat_div, Computable.list_length, Primrec.encode_iff, Primrec.fin_val_iff, Nat.Partrec'.part_iff, Primrec.decode, Nat.Partrec.Code.primrec₂_curry, ComputablePred.halting_problem, Nat.Partrec.Code.eval_part, Nat.Partrec'.part_iff₂, Primrec.nat_sub, Primrec.nat_max, Nat.Partrec'.vec_iff, Primrec.nat_iff, manyOneReducible_toNat, Computable.equiv₂, Primrec₂.ofNat_iff, Nat.Primrec'.to_prim, Primrec.nat_double_succ, Primrec.succ, Primrec.dom_denumerable, Primrec.nat_min, Computable.vector_length, Primrec.encdec, Nat.Primrec'.prim_iff₁, manyOneEquiv_toNat, Primrec.vector_length, Primrec.list_getElem?, Primrec.bind_decode_iff, Primrec₂.nat_iff', mem_range_encode, Computable.succ, Primrec₂.natPair, Nat.Primrec'.vec_iff, Nat.Partrec.Code.encode_lt_rfind', Primrec.map_decode_iff, Nat.Partrec.Code.encode_lt_pair, Primrec.list_getD, toNat_manyOneReducible, ComputablePred.halting_problem_re, Computable.nat_div2, Nat.Partrec.Code.smn, Primrec.nat_div2, Partrec.map_encode_iff, Primrec.list_idxOf₁, Partrec₂.unpaired, Primrec.nat_strong_rec, Primrec.list_getI, Computable.pred, Primrec.ofNat_iff, Primrec.nat_sqrt, Nat.Partrec.Code.encode_lt_prec, Nat.Partrec.Code.primrec_const, computable₂_ack, Computable.nat_bodd, Primrec.ofNat, Nat.Partrec'.part_iff₁, toNat_manyOneEquiv, Primrec.pred, Primrec.encode, Primrec.nat_bodd, Nat.Partrec.Code.primrec₂_prec, Primrec.nat_mod, Primrec.list_findIdx
ofEquiv 📖CompOp
4 mathmath: Primrec.of_equiv_symm_iff, Primrec.of_equiv, Primrec.of_equiv_symm, Primrec.of_equiv_iff
option 📖CompOp
28 mathmath: Primrec.option_iget, Computable.list_getElem?, Primrec.option_map₁, Primrec.list_getElem?₁, Computable.decode, Primrec.option_getD_default, Primrec.option_isSome, Computable.bind_decode_iff, Computable.map_decode_iff, Nat.Partrec.Code.primrec_evaln, Computable.option_some_iff, Primrec.decode₂, Primrec.option_getD, Primrec.decode, Computable.option_some, Primrec.option_guard, Primrec.option_some, Primrec.list_getElem?, Primrec.bind_decode_iff, Primrec₂.nat_iff', Primrec.option_some_iff, Primrec.map_decode_iff, Partrec.option_some_iff, Primrec.optionToList, Primrec₂.option_some_iff, Primrec.option_orElse, Primrec.list_head?, Primrec.listLookup
prod 📖CompOp
13 mathmath: Primrec.snd, Primrec₂.curry, Primrec.fst, Primrec.pair, Nat.Partrec.Code.primrec_evaln, Computable.snd, Primrec₂.uncurry, Primrec.unpair, Computable.unpair, Computable.pair, Computable.fst, Primrec₂.pair, Primrec.listLookup
subtype 📖CompOp
4 mathmath: Primrec.subtype_val_iff, Primrec.subtype_mk, Primrec.subtype_val, Computable.subtype_mk
sum 📖CompOp
9 mathmath: disjoin_le, OneOneReducible.disjoin_left, Computable.sumInr, Computable.sumInl, Primrec.sumInl, ManyOneDegree.add_of, disjoin_manyOneReducible, Primrec.sumInr, OneOneReducible.disjoin_right
toEncodable 📖CompOp
124 mathmath: Nat.Partrec.Code.encode_lt_comp, Primrec.dom_bool, Primrec.vector_toList_iff, Primrec.nat_double, Computable.encode_iff, Primrec.option_iget, Computable.encode, Partrec.rfindOpt, Nat.Partrec.Code.primrec_pappAck_step, not_primrec_ack_self, Primrec.list_length, Primrec.list_findIdx₁, Nat.Partrec'.to_part, Primrec.listFilter, Primrec.list_getElem?₁, Primrec.snd, Primrec₂.unpaired, Nat.Partrec.Code.primrec_pappAck, Primrec.subtype_val_iff, Computable.decode, Partrec.sumCasesOn_right, Primrec.dom_finite, Primrec.option_getD_default, Nat.Partrec.Code.computable_recOn, Primrec₂.curry, Primrec.of_equiv_symm_iff, Primrec.dom_fintype, Nat.Partrec.Code.encodeCode_eq, Primrec₂.encode_iff, Primrec.option_isSome, Computable.bind_decode_iff, Primrec.vector_ofFn', Computable.map_decode_iff, Primrec.fst, Partrec.some, ULower.down_computable, Nat.Primrec'.prim_iff, Primrec.of_equiv, primrecPred_iff_primrec_decide, Primrec.vector_tail, Nat.Partrec.Code.primrec_evaln, Nat.Partrec.Code.primrec_rfind', Primrec₂.uncurry, Partrec₂.comp, Primrec.fin_val, Primrec.decode₂, Primrec.fin_succ, Computable.ofOption, Primrec.const, Partrec.nat_iff, Primrec.unpair, Primrec.list_range, Primrec.list_headI, Primrec.sumInl, PrimrecPred.decide, Primrec.ulower_up, Computable.partrec, Primrec.encode_iff, Partrec.nat_casesOn_right, Primrec.fin_val_iff, Nat.Partrec'.part_iff, Primrec.decode, Partrec.const', Primrec.vector_toList, Primrec.nat_iff, Primrec.of_graph, Partrec.sumCasesOn_left, Nat.Primrec'.to_prim, Primrec.nat_double_succ, Primrec.succ, Primrec.dom_denumerable, Primrec.of_equiv_symm, Primrec.encdec, Primrec.list_flatten, Primrec.list_tail, Nat.Primrec'.prim_iff₁, Primrec.option_some, Primrec.fin_curry, Partrec.none, Primrec.vector_length, Primrec.bind_decode_iff, Primrec₂.nat_iff', mem_range_encode, Nat.Primrec'.vec_iff, Primrec.option_some_iff, Nat.Partrec.Code.encode_lt_rfind', Partrec.bind_decode₂_iff, Primrec.map_decode_iff, Partrec.option_some_iff, Primrec.sumInr, Decidable.Partrec.const', Primrec.vector_get', Nat.Partrec.Code.encode_lt_pair, Primrec.ulower_down, Primrec.optionToList, Primrec.nat_div2, Partrec.map_encode_iff, Primrec.list_idxOf₁, Partrec.optionCasesOn_right, Primrec.not, Partrec₂.unpaired, manyOneEquiv_up, Primrec.list_reverse, Primrec.of_equiv_iff, Primrec.ofNat_iff, Partrec.rfind, PrimrecPred.listFilter_listRange, Primrec.fin_curry₁, Primrec.list_head?, Primrec.nat_rec₁, Primrec.nat_sqrt, Nat.Partrec.Code.encode_lt_prec, Primrec.subtype_val, Nat.Partrec.Code.primrec_const, Primrec.id, Primrec.ofNat, Nat.Partrec'.part_iff₁, prim, Primrec.vector_head, Primrec.pred, Primrec.encode, Partrec.sumCasesOn, Primrec.nat_bodd, Primrec₂.nat_iff
ulower 📖CompOp
4 mathmath: ULower.down_computable, Primrec.ulower_up, Primrec.ulower_down, manyOneEquiv_up
unit 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
mem_range_encode 📖mathematicalPrimrecPred
ofDenumerable
Denumerable.nat
Set
Set.instMembership
Set.range
Encodable.encode
toEncodable
PrimrecPred.not
PrimrecRel.comp
Primrec.eq
Primrec.option_bind
Primrec.decode
Primrec.ite
Primrec.comp
Primrec.encode
Primrec.snd
Primrec.fst
Primrec.option_some
Primrec.const
PrimrecPred.of_eq
Encodable.decode₂_ne_none_iff
prim 📖mathematicalEncodable.encode
Option.encodable
toEncodable
Encodable.decode

Primrec

Definitions

NameCategoryTheorems
PrimrecBounded 📖MathDef

Theorems

NameKindAssumesProvesValidatesDepends On
and 📖mathematicalPrimrec₂
Primcodable.bool
dom_bool₂
beq 📖mathematicalPrimrec₂
Primcodable.bool
PrimrecRel.decide
eq
bind_decode_iff 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primcodable.option
Encodable.decode
Primcodable.toEncodable
Option.bind_congr'
Encodable.encodek
Primrec₂.comp
fst
comp
encode
snd
option_bind
decode
comp 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Nat.Primrec.of_eq
Nat.Primrec.pred
Primcodable.prim
Encodable.encodek
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
comp₂ 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primrec₂
comp
cond 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
of_eq
encode_iff
to₂
comp
fst
const 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Nat.Primrec.of_eq
Nat.Primrec.const
Primcodable.prim
decode 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
Primcodable.prim
decode₂ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode₂
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
option_bind
decode
option_guard
PrimrecRel.comp₂
eq
encode_iff
snd
comp
fst
dom_bool 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.bool
of_eq
cond
id
const
dom_bool₂ 📖mathematicalPrimrec₂
Primcodable.bool
of_eq
cond
fst
comp
dom_bool
snd
dom_denumerable 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.ofDenumerable
Denumerable.ofNat
Nat.Primrec.of_eq
Nat.Primrec.pred
Denumerable.decode_eq_ofNat
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
dom_finite 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Finite.exists_univ_list
option_some_iff
of_eq
comp
list_getElem?₁
list_idxOf₁
List.getElem?_idxOf
dom_fintype 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
dom_finite
encdec 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
nat_iff
Primcodable.prim
encode 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Nat.Primrec.of_eq
Primcodable.prim
encode_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Nat.Primrec.of_eq
comp
encode
eq 📖mathematicalPrimrecRelPrimrecPred.of_eq
PrimrecPred.and
nat_le
PrimrecRel.swap
PrimrecRel.of_eq
Primrec₂.primrecRel
Primrec₂.comp₂
PrimrecRel.decide
comp₂
encode
Primrec₂.left
Primrec₂.right
Encodable.encode_injective
fin_succ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.fin
Encodable.decode
fin_val_iff
comp
succ
fin_val
fin_val 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primcodable.fin
fin_val_iff
id
fin_val_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primcodable.fin
subtype_val_iff
of_equiv_iff
fst 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
Nat.Primrec.of_eq
Nat.Primrec.casesOn'
Primcodable.prim
Nat.unpair_pair
Encodable.decode_prod_val
id 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Nat.Primrec.of_eq
Primcodable.prim
ite 📖PrimrecPred
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
cond
PrimrecPred.decide
list_findIdx₁ 📖mathematicalPrimrec₂
Primcodable.bool
Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
const
of_eq
cond
Primrec₂.comp
id
comp
succ
list_getElem?₁ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
dom_denumerable
Nat.Primrec.of_eq
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
Nat.instCanonicallyOrderedAdd
Nat.instZeroLEOneClass
list_idxOf₁ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
list_findIdx₁
Primrec₂.swap
beq
map_decode_iff 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primcodable.option
Encodable.decode
Primcodable.toEncodable
bind_decode_iff
Primrec₂.option_some_iff
nat_add 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.unpaired'
Nat.Primrec.add
nat_bodd 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Nat.bodd
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
of_eq
Primrec₂.comp
beq
nat_mod
id
const
Nat.mod_two_of_bodd
instLawfulBCmpCompare_mathlib
nat_casesOn 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primrec₂
Primrec₂.comp
nat_casesOn'
id
nat_casesOn' 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.comp₂
Primrec₂.left
comp₂
fst
Primrec₂.right
nat_casesOn₁ 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
id
const
comp₂
Primrec₂.right
nat_div 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
of_graph
fst
PrimrecPred.or
PrimrecPred.and
PrimrecRel.comp
eq
comp
snd
const
nat_lt
nat_le
Primrec₂.comp
nat_mul
succ
PrimrecRel.of_eq
MulZeroClass.mul_zero
Nat.instCanonicallyOrderedAdd
le_antisymm_iff
nat_div2 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Nat.div2
Encodable.decode
of_eq
Primrec₂.comp
nat_div
id
const
Nat.div2_val
nat_double 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primrec₂.comp
nat_mul
const
id
nat_double_succ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
comp
succ
nat_double
nat_findGreatest 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
PrimrecRel
Nat.findGreatestof_eq
nat_rec'
const
ite
PrimrecRel.comp
fst
comp
succ
snd
nat_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
dom_denumerable
nat_iterate 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primrec₂
Nat.iterateof_eq
nat_rec'
Primrec₂.comp₂
Primrec₂.left
comp₂
snd
Primrec₂.right
Function.iterate_succ'
nat_le 📖mathematicalPrimrecRel
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.primrecRel
of_eq
nat_sub
const
to₂
not_le
nat_lt 📖mathematicalPrimrecRel
Primcodable.ofDenumerable
Denumerable.nat
PrimrecPred.of_eq
PrimrecPred.not
PrimrecRel.comp
nat_le
snd
fst
nat_max 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
ite
PrimrecRel.comp
nat_le
fst
snd
nat_min 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
ite
nat_le
fst
snd
nat_mod 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.of_eq
to₂
Primrec₂.comp
nat_sub
fst
nat_mul
snd
nat_div
add_comm
nat_mul 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.unpaired'
Nat.Primrec.mul
nat_rec 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primrec₂
Primcodable.prod
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.nat_iff
Nat.Primrec.of_eq
Nat.Primrec.casesOn'
Nat.Primrec.pred
Nat.Primrec.id
Primcodable.prim
Nat.unpair_pair
Encodable.decode_prod_val
Option.bind_congr'
Encodable.encodek
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
nat_rec' 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
Primrec₂
Primcodable.prod
Primrec₂.comp
id
nat_rec₁ 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
nat_rec'
id
const
comp₂
Primrec₂.right
nat_sub 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂.unpaired'
Nat.Primrec.sub
not 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
dom_bool
ofNat 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.ofNat
Encodable.decode
Denumerable.nat
ofNat_iff
id
ofNat_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.ofDenumerable
Denumerable.ofNat
Denumerable.nat
dom_denumerable
nat_iff
encode_iff
of_eq 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
of_equiv 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Encodable.decode
Primcodable.ofEquiv
encode_iff
encode
of_equiv_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Encodable.decode
Primcodable.ofEquiv
of_eq
comp
of_equiv_symm
Equiv.symm_apply_apply
of_equiv
of_equiv_symm 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofEquiv
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
Encodable.decode
encode_iff
Equiv.apply_symm_apply
of_equiv_symm_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofEquiv
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
Encodable.decode
of_eq
comp
of_equiv
Equiv.apply_symm_apply
of_equiv_symm
of_graph 📖mathematicalPrimrecBounded
Primcodable.ofDenumerable
Denumerable.nat
PrimrecRel
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
of_eq
nat_findGreatest
Nat.findGreatest_spec
option_bind 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Primrec₂
of_eq
const
option_bind₁ 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
option_bind
id
to₂
comp
snd
option_casesOn 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Primrec₂
encode_iff
of_eq
comp₂
pred
Primrec₂.encode_iff
Primrec₂.comp₂
Primrec₂.nat_iff'
to₂
comp
encode
fst
Primrec₂.right
Option.bind_congr'
Encodable.encodek
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
option_get 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Nat.Primrec.of_eq
Nat.Primrec.pred
Nat.instCanonicallyOrderedAdd
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
option_getD 📖mathematicalPrimrec₂
Primcodable.option
of_eq
Primrec₂.left
Primrec₂.right
option_getD_default 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.option
Primrec₂.comp
option_getD
id
const
option_guard 📖mathematicalPrimrecRel
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.optionite
PrimrecRel.comp
id
option_some_iff
const
option_iget 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Option.iget
Encodable.decode
Primcodable.option
option_getD_default
option_isSome 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
Primcodable.option
of_eq
id
const
to₂
option_map 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Primrec₂
of_eq
option_bind
comp₂
option_some
option_map₁ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.optionoption_map
id
to₂
comp
snd
option_orElse 📖mathematicalPrimrec₂
Primcodable.option
of_eq
fst
snd
to₂
comp
option_some 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
Nat.Primrec.of_eq
Primcodable.prim
option_some_iff 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.option
Encodable.decode
encode_iff
comp
pred
option_some
or 📖mathematicalPrimrec₂
Primcodable.bool
dom_bool₂
pair 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prodNat.Primrec.of_eq
Nat.Primrec.pred
Primcodable.prim
Encodable.encodek
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
pred 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
nat_iff
Nat.Primrec.pred
primrecPred 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
PrimrecPred
snd 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
Nat.Primrec.of_eq
Nat.Primrec.casesOn'
Primcodable.prim
Nat.unpair_pair
Encodable.decode_prod_val
subtype_mk 📖mathematicalPrimrecPred
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.subtypesubtype_val_iff
subtype_val 📖mathematicalPrimrecPredEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.subtype
Nat.Primrec.of_eq
Primcodable.prim
subtype_val_iff 📖mathematicalPrimrecPredEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.subtype
Nat.Primrec.of_eq
comp
subtype_val
succ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.ofDenumerable
Denumerable.nat
Encodable.decode
nat_iff
sumCasesOn 📖Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.sum
Encodable.decode
Primrec₂
option_some_iff
of_eq
cond
comp
nat_bodd
encode_iff
option_map
decode
nat_div2
Nat.bodd_mul
Nat.bodd_succ
Nat.div2_val
mul_div_cancel_left₀
Nat.instMulDivCancelClass
Nat.instCharZero
Nat.instAtLeastTwoHAddOfNat
Encodable.encodek
Nat.div2_succ
sumInl 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.sum
Encodable.decode
encode_iff
comp
nat_double
encode
sumInr 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.sum
Encodable.decode
encode_iff
comp
nat_double_succ
encode
to₂ 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
Primrec₂
ulower_down 📖mathematicalEncodable.encode
ULower
Primcodable.toEncodable
Option.encodable
Primcodable.ulower
ULower.down
Encodable.decode
Primcodable.mem_range_encode
encode
ulower_up 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
ULower
ULower.up
Encodable.decode
Primcodable.ulower
option_get
comp
decode₂
subtype_val
Primcodable.mem_range_encode
unpair 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.prod
Primcodable.ofDenumerable
Denumerable.nat
Nat.unpair
Encodable.decode
of_eq
pair
nat_iff

PrimrecPred

Theorems

NameKindAssumesProvesValidatesDepends On
and 📖PrimrecPredPrimrec.primrecPred
Primrec.of_eq
Primrec₂.comp
Primrec.and
comp 📖PrimrecPred
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primrec.primrecPred
Primrec.comp
decide 📖mathematicalPrimrecPredEncodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonDecidable
not 📖PrimrecPredPrimrec.primrecPred
Primrec.of_eq
Primrec.comp
Primrec.not
of_eq 📖PrimrecPred
or 📖PrimrecPredPrimrec.primrecPred
Primrec.of_eq
Primrec₂.comp
Primrec.or
primrecRel 📖mathematicalPrimrecPred
Primcodable.prod
PrimrecRel

PrimrecRel

Theorems

NameKindAssumesProvesValidatesDepends On
comp 📖mathematicalPrimrecRel
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
PrimrecPredPrimrecPred.comp
Primrec.pair
comp₂ 📖PrimrecRel
Primrec₂
comp
decide 📖mathematicalPrimrecRelPrimrec₂
Primcodable.bool
PrimrecPred.decide
not 📖PrimrecRelPrimrecPred.not
of_eq 📖PrimrecRel
swap 📖mathematicalPrimrecRelFunction.swapcomp₂
Primrec₂.right
Primrec₂.left

Primrec₂

Theorems

NameKindAssumesProvesValidatesDepends On
comp 📖Primrec₂
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primrec.comp
Primrec.pair
comp₂ 📖Primrec₂comp
const 📖mathematicalPrimrec₂Primrec.const
curry 📖mathematicalPrimrec₂
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
uncurry
encode_iff 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Encodable.encode
Primcodable.toEncodable
Primrec.encode_iff
left 📖mathematicalPrimrec₂Primrec.fst
mk 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
Primrec₂
natPair 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Nat.pair
Denumerable.decode_eq_ofNat
Denumerable.ofEquiv_ofNat
Denumerable.sigma_ofNat_val
Nat.pair_unpair
nat_iff 📖mathematicalPrimrec₂
Nat.unpaired
Encodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Encodable.decode_prod_val
nat_iff' 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primcodable.option
Encodable.decode
Primcodable.toEncodable
nat_iff
unpaired'
encode_iff
ofNat_iff 📖mathematicalPrimrec₂
Primcodable.ofDenumerable
Denumerable.nat
Denumerable.ofNat
Primrec.ofNat_iff
Denumerable.ofEquiv_ofNat
Denumerable.sigma_ofNat_val
unpaired
of_eq 📖Primrec₂
option_some_iff 📖mathematicalPrimrec₂
Primcodable.option
Primrec.option_some_iff
pair 📖mathematicalPrimrec₂
Primcodable.prod
Primrec.pair
Primrec.fst
Primrec.snd
primrecRel 📖mathematicalPrimrec₂
Primcodable.bool
PrimrecRelPrimrec.primrecPred
right 📖mathematicalPrimrec₂Primrec.snd
swap 📖mathematicalPrimrec₂Function.swapcomp₂
right
left
uncurry 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Encodable.decode
Primcodable.prod
Primrec₂
unpaired 📖mathematicalEncodable.encode
Option.encodable
Primcodable.toEncodable
Nat.unpaired
Encodable.decode
Primcodable.ofDenumerable
Denumerable.nat
Primrec₂
Nat.unpair_pair
Primrec.comp
natPair
Primrec.unpair
unpaired' 📖mathematicalNat.unpaired
Primrec₂
Primcodable.ofDenumerable
Denumerable.nat
Primrec.nat_iff
unpaired

(root)

Definitions

NameCategoryTheorems
Primcodable 📖CompData
PrimrecPred 📖MathDef
4 mathmath: PrimrecRel.comp, Primrec.primrecPred, primrecPred_iff_primrec_decide, Primcodable.mem_range_encode
PrimrecRel 📖MathDef
6 mathmath: Primrec.nat_lt, Primrec.eq, Primrec.nat_le, primrecRel_iff_primrec_decide, PrimrecPred.primrecRel, Primrec₂.primrecRel
Primrec₂ 📖MathDef
53 mathmath: Primrec₂.left, Primrec.nat_add, Primrec.and, Primrec₂.unpaired, not_primrec₂_ack, Nat.Partrec.Code.primrec₂_comp, Primrec.list_idxOf, PrimrecRel.listFilter, Primrec₂.curry, Primrec.beq, Primrec₂.encode_iff, Primrec₂.unpaired', Nat.Primrec'.prim_iff₂, Primrec.nat_mul, Primrec.dom_bool₂, Primrec₂.mk, Primrec.list_concat, Primrec₂.right, Primrec₂.uncurry, Nat.Partrec.Code.primrec₂_pair, primrecRel_iff_primrec_decide, Primrec.vector_get, Primrec.nat_div, Primrec.option_getD, Nat.Partrec.Code.primrec₂_curry, Primrec.list_cons, Primrec₂.const, Primrec.nat_sub, Primrec.nat_max, Primrec.vector_cons, Primrec₂.ofNat_iff, Primrec.nat_min, Primrec.fin_curry, Primrec.list_getElem?, Primrec.bind_decode_iff, Primrec₂.nat_iff', Primrec₂.natPair, Primrec.map_decode_iff, Primrec.list_getD, Primrec.or, Primrec₂.pair, Primrec₂.option_some_iff, Primrec.option_orElse, Primrec.list_getI, Primrec.fin_curry₁, PrimrecRel.decide, Primrec.fin_app, Primrec.to₂, Primrec.list_append, Primrec.listLookup, Nat.Partrec.Code.primrec₂_prec, Primrec₂.nat_iff, Primrec.nat_mod

Theorems

NameKindAssumesProvesValidatesDepends On
primrecPred_iff_primrec_decide 📖mathematicalPrimrecPred
Encodable.encode
Option.encodable
Primcodable.toEncodable
Primcodable.bool
Encodable.decode
PrimrecPred.decide
Primrec.primrecPred
primrecRel_iff_primrec_decide 📖mathematicalPrimrecRel
Primrec₂
Primcodable.bool
PrimrecRel.decide
Primrec₂.primrecRel

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