Documentation Verification Report

Rot

📁 Source: BanachTarski/Rot.lean

Statistics

MetricCount
DefinitionsBasis3, COB, COB_MB, COB_mat, PROD_BLOCK, ang_diff, ax_B, ax_space, choice_set, fTS_fun, finToSigma, mod_dim, mod_dim_decidableEq, mod_dim_fintype, operp, orth, orth_B, plane_o, rot, rot_by_parts, rot_iso, rot_iso_plane_equiv, rot_iso_plane_to_st, rot_mat, rot_mat_block_1, rot_mat_block_2, rot_mat_inner, rot_mat_inner_trans, sm_bases, spar, submods, tmp_basis, up, x_B, x_B_c
35
TheoremsCOB_MB_is_ortho, COB_mat_is_ortho, COB_to_basis, R3_dim_3, block_1_lem, block_2_lem, block_repr, cob_mat_other_repr, el_by_parts, fTS_fun_bij, hf, inner_as_to_matrix, inner_as_to_matrix_MB, internal_pr, operp_add, operp_of_ax_space, operp_spar, operp_up, operp_up_2, orth_dim_2, orth_dim_3, orth_nonempty, orth_toMatrix_mulVec_repr, rips_add, rmi_trans_equiv, rot_by_parts_comp, rot_comp_add, rot_iso_comp, rot_iso_fixed_back, rot_iso_pow_lemma, rot_mat_block_prop, rot_mat_comp_add, rot_mat_inner_comp_add, rot_mat_inner_is_special, rot_mat_is_special, rot_pow_lemma, s2_nonzero, same_action, spar_add, spar_of_ax_space, spar_of_orth, spar_operp, spar_spar, spar_up_2, spar_up_rot, triv_rot, triv_rot_by_parts, triv_rot_inner, triv_rot_iso, up_mem, x_B_nz
51
Total86

(root)

Definitions

NameCategoryTheorems
Basis3 📖CompOp
1 mathmath: cob_mat_other_repr
COB 📖CompOp
3 mathmath: COB_to_basis, cob_mat_other_repr, inner_as_to_matrix
COB_MB 📖CompOp
3 mathmath: COB_MB_is_ortho, COB_to_basis, inner_as_to_matrix_MB
COB_mat 📖CompOp
2 mathmath: COB_mat_is_ortho, cob_mat_other_repr
PROD_BLOCK 📖CompOp
ang_diff 📖CompOp
2 mathmath: BadAtN_rot_iso_equiv, rot_iso_fixed_gen
ax_B 📖CompOp
ax_space 📖CompOp
choice_set 📖CompOp
1 mathmath: orth_nonempty
fTS_fun 📖CompOp
1 mathmath: fTS_fun_bij
finToSigma 📖CompOp
mod_dim 📖CompOp
4 mathmath: block_1_lem, fTS_fun_bij, block_repr, block_2_lem
mod_dim_decidableEq 📖CompOp
3 mathmath: block_1_lem, block_repr, block_2_lem
mod_dim_fintype 📖CompOp
3 mathmath: block_1_lem, block_repr, block_2_lem
operp 📖CompOp
7 mathmath: operp_of_ax_space, operp_up_2, operp_add, spar_operp, el_by_parts, operp_up, operp_spar
orth 📖CompOp
14 mathmath: spar_up_rot, orth_nonempty, orth_dim_2, spar_up_2, operp_of_ax_space, rips_add, operp_up_2, triv_rot_inner, up_mem, operp_add, spar_operp, el_by_parts, operp_up, operp_spar
orth_B 📖CompOp
plane_o 📖CompOp
rot 📖CompOp
8 mathmath: countable_bad_rots, rot_containment_general, bad_as_union_rot, triv_rot, rot_pow_lemma, rot_comp_add, same_action, rot_containment_S2
rot_by_parts 📖CompOp
2 mathmath: triv_rot_by_parts, rot_by_parts_comp
rot_iso 📖CompOp
13 mathmath: rot_iso_pow_lemma, hf, rot_iso_fixed_back, rot_iso_comp_add, triv_rot_iso, block_1_lem, same_action, inner_as_to_matrix_MB, inner_as_to_matrix, rot_iso_power_lemma, block_repr, rot_iso_comp, block_2_lem
rot_iso_plane_equiv 📖CompOp
rot_iso_plane_to_st 📖CompOp
2 mathmath: rips_add, triv_rot_inner
rot_mat 📖CompOp
2 mathmath: rot_mat_is_special, rot_mat_comp_add
rot_mat_block_1 📖CompOp
1 mathmath: rot_mat_block_prop
rot_mat_block_2 📖CompOp
1 mathmath: rot_mat_block_prop
rot_mat_inner 📖CompOp
5 mathmath: rmi_trans_equiv, rot_mat_inner_is_special, rot_mat_inner_comp_add, inner_as_to_matrix_MB, inner_as_to_matrix
rot_mat_inner_trans 📖CompOp
1 mathmath: rmi_trans_equiv
sm_bases 📖CompOp
3 mathmath: block_1_lem, block_repr, block_2_lem
spar 📖CompOp
9 mathmath: spar_up_rot, spar_add, spar_up_2, spar_of_ax_space, spar_of_orth, spar_operp, spar_spar, el_by_parts, operp_spar
submods 📖CompOp
5 mathmath: hf, internal_pr, block_1_lem, block_repr, block_2_lem
tmp_basis 📖CompOp
up 📖CompOp
3 mathmath: spar_up_rot, up_mem, operp_up
x_B 📖CompOp
x_B_c 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
COB_MB_is_ortho 📖mathematicalR3
COB_MB
orth_dim_2
x_B_nz
internal_pr
COB_MB.eq_1
COB_mat_is_ortho 📖mathematicalMAT
COB_mat
cob_mat_other_repr
COB_to_basis 📖mathematicalR3
COB
COB_MB
COB_MB_is_ortho
R3_dim_3 📖mathematicalR3
block_1_lem 📖mathematicalR3
submods
mod_dim
mod_dim_fintype
mod_dim_decidableEq
sm_bases
rot_iso
hf
hf
orth_dim_2
spar_up_2
operp_up_2
x_B_nz
block_2_lem 📖mathematicalR3
submods
mod_dim
mod_dim_fintype
mod_dim_decidableEq
sm_bases
rot_iso
hf
hf
spar_of_ax_space
operp_of_ax_space
block_repr 📖mathematicalR3
mod_dim
mod_dim_fintype
mod_dim_decidableEq
submods
internal_pr
sm_bases
rot_iso
rot_mat_block_prop
hf
internal_pr
block_2_lem
block_1_lem
cob_mat_other_repr 📖mathematicalCOB_mat
R3
COB
Basis3
el_by_parts 📖mathematicalR3
orth
operp
spar
fTS_fun_bij 📖mathematicalmod_dim
fTS_fun
hf 📖mathematicalR3
rot_iso
submods
spar_of_orth
up_mem
operp_of_ax_space
spar_of_ax_space
inner_as_to_matrix 📖mathematicalrot_mat_inner
R3
COB
rot_iso
COB_to_basis
inner_as_to_matrix_MB
inner_as_to_matrix_MB 📖mathematicalrot_mat_inner
R3
COB_MB
rot_iso
internal_pr
block_repr
fTS_fun_bij
internal_pr 📖mathematicalR3
submods
operp_add 📖mathematicaloperp
R3
orth
operp_of_ax_space 📖mathematicalR3
ax_space
operp
orth
operp_spar 📖mathematicaloperp
spar
R3
orth
operp_up 📖mathematicaloperp
R3
orth
up
operp_up_2 📖mathematicaloperp
R3
orth
orth_dim_2 📖mathematicalR3
orth
R3_dim_3
s2_nonzero
orth_dim_3 📖mathematicalR3
orth_nonempty 📖mathematicalR3
orth
choice_set
orth_toMatrix_mulVec_repr 📖mathematicalR3
rips_add 📖mathematicalR3
orth
rot_iso_plane_to_st
orth_dim_2
rmi_trans_equiv 📖mathematicalrot_mat_inner
rot_mat_inner_trans
rot_by_parts_comp 📖mathematicalrot_by_partsoperp_add
spar_add
operp_up
operp_spar
spar_up_rot
spar_spar
rips_add
rot_comp_add 📖mathematicalR3
f
SO3
SO3_action_on_R3
rot
rot_mat_comp_add
rot_iso_comp 📖mathematicalR3
rot_iso
rot_by_parts_comp
rot_iso_fixed_back 📖mathematicalR3
rot_iso
orth_dim_2
el_by_parts
rot_iso_pow_lemma 📖mathematicalR3
rot_iso
triv_rot_iso
rot_iso_comp
rot_mat_block_prop 📖mathematicalrot_mat_block_1
rot_mat_block_2
internal_pr
hf
rot_mat_comp_add 📖mathematicalMAT
rot_mat
COB_mat_is_ortho
unitary_invs_coe
rot_mat_inner_comp_add
rot_mat_inner_comp_add 📖mathematicalMAT
rot_mat_inner
rot_mat_inner_is_special 📖mathematicalMAT
SO3
rot_mat_inner
rmi_trans_equiv
rot_mat_is_special 📖mathematicalMAT
SO3
rot_mat
rot_mat_inner_is_special
COB_mat_is_ortho
unitary_invs_coe
cob_mat_other_repr
rot_pow_lemma 📖mathematicalR3
f
SO3
SO3_action_on_R3
rot
triv_rot
rot_comp_add
s2_nonzero 📖
same_action 📖mathematicalSO3
R3
rot
rot_iso
orth_toMatrix_mulVec_repr
inner_as_to_matrix
spar_add 📖mathematicalspar
R3
spar_of_ax_space 📖mathematicalR3
ax_space
spar
spar_of_orth 📖mathematicalR3
orth
spar
spar_operp 📖mathematicalspar
R3
orth
operp
spar_spar 📖mathematicalspar
spar_up_2 📖mathematicalspar
R3
orth
spar_of_orth
spar_up_rot 📖mathematicalspar
R3
orth
up
spar_of_orth
triv_rot 📖mathematicalrot
SO3
rot_mat_is_special
COB_mat_is_ortho
unitary_invs_coe
triv_rot_by_parts 📖mathematicalrot_by_parts
R3
triv_rot_inner
el_by_parts
triv_rot_inner 📖mathematicalrot_iso_plane_to_st
R3
orth
orth_dim_2
triv_rot_iso 📖mathematicalrot_iso
R3
triv_rot_inner
el_by_parts
up_mem 📖mathematicalR3
orth
up
x_B_nz 📖

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