Documentation Verification Report

Core

📁 Source: Mathlib/Tactic/CancelDenoms/Core.lean

Statistics

Metric	Count
Definitions `CancelResult`, `cancelled`, `pf`, `cancelDenominatorsInType`, `derive`, `deriveThms`, `findCancelFactor`, `findCompLemma`, `mkProdPrf`, `cancelDenoms`, `tacticCancel_denoms_`	11
Theorems `add_subst`, `cancel_factors_eq`, `cancel_factors_eq_div`, `cancel_factors_le`, `cancel_factors_lt`, `cancel_factors_ne`, `derive_trans`, `derive_trans₂`, `div_subst`, `inv_subst`, `mul_subst`, `neg_subst`, `pow_subst`, `sub_subst`	14
Total	25

Mathlib.Tactic

Definitions

Name	Category	Theorems
`cancelDenoms` 📖	CompOp	—
`tacticCancel_denoms_` 📖	CompOp	—

Mathlib.Tactic.CancelDenoms

Definitions

Name	Category	Theorems
`CancelResult` 📖	CompData	—
`cancelDenominatorsInType` 📖	CompOp	—
`derive` 📖	CompOp	—
`deriveThms` 📖	CompOp	—
`findCancelFactor` 📖	CompOp	—
`findCompLemma` 📖	CompOp	—
`mkProdPrf` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`add_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Distrib.toAdd`	—	`left_distrib` `Distrib.leftDistribClass`
`cancel_factors_eq` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `DivisionRing.toRing`	—	—
`cancel_factors_eq_div` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing`	`DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing`	—	`eq_div_of_mul_eq` `mul_comm`
`cancel_factors_le` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `Preorder.toLT` `PartialOrder.toPreorder` `SemilatticeInf.toPartialOrder` `Lattice.toSemilatticeInf` `DistribLattice.toLattice` `instDistribLatticeOfLinearOrder` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass`	`Preorder.toLE` `PartialOrder.toPreorder` `SemilatticeInf.toPartialOrder` `Lattice.toSemilatticeInf` `DistribLattice.toLattice` `instDistribLatticeOfLinearOrder` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `DivisionRing.toRing`	—	`mul_le_mul_iff_right₀` `IsOrderedRing.toPosMulMono` `IsStrictOrderedRing.toIsOrderedRing` `PosMulStrictMono.toPosMulReflectLE` `IsStrictOrderedRing.toPosMulStrictMono` `one_div_pos` `PosMulReflectLE.toPosMulReflectLT` `mul_assoc` `mul_comm` `mul_pos`
`cancel_factors_lt` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `Preorder.toLT` `PartialOrder.toPreorder` `SemilatticeInf.toPartialOrder` `Lattice.toSemilatticeInf` `DistribLattice.toLattice` `instDistribLatticeOfLinearOrder` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass`	`Preorder.toLT` `PartialOrder.toPreorder` `SemilatticeInf.toPartialOrder` `Lattice.toSemilatticeInf` `DistribLattice.toLattice` `instDistribLatticeOfLinearOrder` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `DivisionRing.toRing`	—	`mul_lt_mul_iff_right₀` `IsStrictOrderedRing.toPosMulStrictMono` `PosMulReflectLE.toPosMulReflectLT` `PosMulStrictMono.toPosMulReflectLE` `one_div_pos` `mul_assoc` `mul_comm` `mul_pos`
`cancel_factors_ne` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `DivisionRing.toRing`	—	`not_iff_not` `cancel_factors_eq`
`derive_trans` 📖	—	—	—	—	—
`derive_trans₂` 📖	—	—	—	—	—
`div_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `DivisionRing.toRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `Field.toDivisionRing`	—	`mul_assoc` `mul_div_left_comm` `mul_comm` `one_mul`
`inv_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Field.toCommRing` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroupWithZero.toDivisionCommMonoid` `Semifield.toCommGroupWithZero` `Field.toSemifield`	—	`div_eq_mul_inv` `mul_div_cancel_right₀` `GroupWithZero.toMulDivCancelClass`
`mul_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing`	—	`mul_comm` `mul_assoc`
`neg_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `Ring.toAddCommGroup`	—	`mul_neg`
`pow_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Monoid.toPow` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `CommSemiring.toSemiring` `CommRing.toCommSemiring`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `CommRing.toNonUnitalCommRing` `Monoid.toPow` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `CommSemiring.toSemiring` `CommRing.toCommSemiring`	—	`mul_pow` `mul_assoc`
`sub_subst` 📖	mathematical	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddGroupWithOne.toAddGroup` `Ring.toAddGroupWithOne`	—	`sub_eq_add_neg` `left_distrib` `Distrib.leftDistribClass` `mul_neg`

Mathlib.Tactic.CancelDenoms.CancelResult

Definitions

Name	Category	Theorems
`cancelled` 📖	CompOp	—
`pf` 📖	CompOp	—

---

← Back to Index