module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\na : Rˣ\nha : ↑a ∈ P\nthis : ↑a * (↑a⁻¹ * ↑a⁻¹) ∈ P\n⊢ ↑a⁻¹ ∈ P",
"usedConstants": [
"Units.val",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Membership.mem",
"Units",
"Eq.mp",
"id",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 10
} | [
{
"pp": "F : Type u_2\ninst✝ : Field F\nP : RingPreordering F\na : F\nha : a ∈ P\nmem : 1 / a ∈ P\n⊢ a⁻¹ ∈ P",
"usedConstants": [
"DivInvMonoid.toInv",
"instHDiv",
"InvOneClass.toOne",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Quotient | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 12
} | [
{
"pp": "α : Type u_1\ns : Setoid α\ninst✝ : LinearOrder α\nH : ∀ (x : Quotient s), (Quotient.mk s ⁻¹' {x}).OrdConnected\nx y : α\n⊢ (⟦x⟧ ≤ ⟦y⟧) = (x ≤ y ∨ x ≈ y)",
"usedConstants": []
}
] | revert x y | Lean.Elab.Tactic.evalRevert | Lean.Parser.Tactic.revert |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 370,
"column": 35
} | {
"line": 370,
"column": 58
} | [
{
"pp": "K : Type u\ninst✝ : Field K\nA R S : ValuationSubring K\nhR : A ≤ R\nhS : A ≤ S\nh : R ≤ S\nx : ↥A\nhx : x ∈ A.idealOfLE S hS\nc : 1 ≤ (R.mapOfLE S h) (R.valuation ↑((A.inclusion R hR) x))\n⊢ False",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.to... | mapOfLE_valuation_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 414,
"column": 4
} | {
"line": 414,
"column": 12
} | [
{
"pp": "case inl\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nh : A.primeSpectrumEquiv (A.primeSpectrumEquiv.symm ⟨B, hle⟩) = A.primeSpectrumEquiv ⊥\n⊢ A = B ∨ B = ⊤",
"usedConstants": [
"Subtype.mk.congr_simp",
"Valua... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 414,
"column": 4
} | {
"line": 414,
"column": 12
} | [
{
"pp": "case inr\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nh : A.primeSpectrumEquiv (A.primeSpectrumEquiv.symm ⟨B, hle⟩) = A.primeSpectrumEquiv ⊤\n⊢ A = B ∨ B = ⊤",
"usedConstants": [
"Subtype.mk.congr_simp",
"Valua... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 417,
"column": 50
} | {
"line": 417,
"column": 58
} | [
{
"pp": "case inl\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nhTop : B ≠ ⊤\nh : A = B\n⊢ A = B",
"usedConstants": [
"congrArg",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.tran... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 417,
"column": 50
} | {
"line": 417,
"column": 58
} | [
{
"pp": "case inr\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nhTop : B ≠ ⊤\nh : B = ⊤\n⊢ A = B",
"usedConstants": [
"False",
"congrArg",
"False.elim",
"Eq.mp",
"not_true_eq_false",
"Ne",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 420,
"column": 50
} | {
"line": 420,
"column": 58
} | [
{
"pp": "case inl\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nhne : A ≠ B\nh : A = B\n⊢ B = ⊤",
"usedConstants": [
"False",
"congrArg",
"False.elim",
"Eq.mp",
"not_true_eq_false",
"Ne",
"T... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 420,
"column": 50
} | {
"line": 420,
"column": 58
} | [
{
"pp": "case inr\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhle : A ≤ B\nhne : A ≠ B\nh : B = ⊤\n⊢ B = ⊤",
"usedConstants": [
"congrArg",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"ValuationSubring.ins... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 423,
"column": 53
} | {
"line": 423,
"column": 61
} | [
{
"pp": "case inl\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhlt : A < B\nh : A = B\n⊢ B = ⊤",
"usedConstants": [
"False",
"ValuationSubring.instPartialOrder",
"Preorder.toLT",
"congrArg",
"False.elim",
"Pa... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 423,
"column": 53
} | {
"line": 423,
"column": 61
} | [
{
"pp": "case inr\nK : Type u\ninst✝¹ : Field K\nA : ValuationSubring K\ninst✝ : Ring.KrullDimLE 1 ↥A\nB : ValuationSubring K\nhlt : A < B\nh : B = ⊤\n⊢ B = ⊤",
"usedConstants": [
"congrArg",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"ValuationSubring.instTop",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 957,
"column": 2
} | {
"line": 957,
"column": 63
} | [
{
"pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst... | simp_rw [LinearMap.mem_range, LinearPMap.toFun_eq_coe] at ⊢ h | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 528,
"column": 6
} | {
"line": 528,
"column": 60
} | [
{
"pp": "case neg.inr\nK : Type u\ninst✝ : Field K\nA B : ValuationSubring K\nh : A.unitGroup ≤ B.unitGroup\nx : K\nh_1 : ¬x = 0\nh_2 : ¬1 + x = 0\nhx : A.valuation x = 1\n⊢ x ∈ B",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"ValuationSubring.unitGroup",
"DivisionSemiring.toGroup... | have := h (show Units.mk0 x h_1 ∈ A.unitGroup from hx) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 528,
"column": 6
} | {
"line": 529,
"column": 63
} | [
{
"pp": "case neg.inr\nK : Type u\ninst✝ : Field K\nA B : ValuationSubring K\nh : A.unitGroup ≤ B.unitGroup\nx : K\nh_1 : ¬x = 0\nh_2 : ¬1 + x = 0\nhx : A.valuation x = 1\n⊢ x ∈ B",
"usedConstants": [
"Units.val",
"GroupWithZero.toMonoidWithZero",
"ValuationSubring.unitGroup",
"MulEq... | have := h (show Units.mk0 x h_1 ∈ A.unitGroup from hx)
exact SetLike.coe_mem (B.unitGroupMulEquiv ⟨_, this⟩ : B) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.ValuationSubring | {
"line": 528,
"column": 6
} | {
"line": 529,
"column": 63
} | [
{
"pp": "case neg.inr\nK : Type u\ninst✝ : Field K\nA B : ValuationSubring K\nh : A.unitGroup ≤ B.unitGroup\nx : K\nh_1 : ¬x = 0\nh_2 : ¬1 + x = 0\nhx : A.valuation x = 1\n⊢ x ∈ B",
"usedConstants": [
"Units.val",
"GroupWithZero.toMonoidWithZero",
"ValuationSubring.unitGroup",
"MulEq... | have := h (show Units.mk0 x h_1 ∈ A.unitGroup from hx)
exact SetLike.coe_mem (B.unitGroupMulEquiv ⟨_, this⟩ : B) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\nb : WithTop α\na : α\nh : (↑a).untop₀ ≤ b.untop₀\nhb : b = ⊤\n⊢ ↑a ≤ b",
"usedConstants": [
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\nb : WithTop α\na : α\nh : (↑a).untop₀ ≤ b.untop₀\nhb : b = ⊤\n⊢ ↑a ≤ b",
"usedConstants": [
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\nb : WithTop α\na : α\nh : (↑a).untop₀ ≤ b.untop₀\nhb : b = ⊤\n⊢ ↑a ≤ b",
"usedConstants": [
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 10
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\na b : α\nh : (↑a).untop₀ ≤ (↑b).untop₀\n⊢ ↑a ≤ ↑b",
"usedConstants": [
"WithTop.coe_le_coe._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"LE.le",
"WithTop.some",
"True",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\na : WithTop α\nb : α\nh : a ≤ ↑b\nha : a = ⊤\n⊢ a.untop₀ ≤ (↑b).untop₀",
"usedConstants": [
"False",
"WithTop.instPartialOrder",
"WithTop.untop₀",
"WithTop.instPreorder",
"congrArg",
"WithTo... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\na : WithTop α\nb : α\nh : a ≤ ↑b\nha : a = ⊤\n⊢ a.untop₀ ≤ (↑b).untop₀",
"usedConstants": [
"False",
"WithTop.instPartialOrder",
"WithTop.untop₀",
"WithTop.instPreorder",
"congrArg",
"WithTo... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\na : WithTop α\nb : α\nh : a ≤ ↑b\nha : a = ⊤\n⊢ a.untop₀ ≤ (↑b).untop₀",
"usedConstants": [
"False",
"WithTop.instPartialOrder",
"WithTop.untop₀",
"WithTop.instPreorder",
"congrArg",
"WithTo... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.WithTop.Untop0 | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 10
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : AddCommGroup α\ninst✝ : PartialOrder α\nb a : α\nh : ↑a ≤ ↑b\n⊢ (↑a).untop₀ ≤ (↑b).untop₀",
"usedConstants": [
"WithTop.coe_le_coe._simp_1",
"WithTop.instPreorder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.mp",
"id",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Pointwise.Stabilizer | {
"line": 48,
"column": 11
} | {
"line": 48,
"column": 23
} | [
{
"pp": "case refine_2\nG : Type u_1\nα : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G α\na : G\ns : Set α\nh : ∀ (b : α), a • b ∈ s ↔ b ∈ s\n⊢ a • s = s",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"_private.Mathlib.Algebra.Pointwise.Stabilizer.0.MulAction.mem_stabilizer_set._simp_1_1",... | Set.ext_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Pointwise.Stabilizer | {
"line": 117,
"column": 6
} | {
"line": 117,
"column": 53
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\na : G\ns : Set G\nha : a ∈ s\nb : G\nhb : b ∈ ↑(stabilizer G s)\n⊢ b * a ∈ s",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Membership.mem",
"id",
"Mu... | by rwa [← smul_eq_mul, mem_stabilizer_set.1 hb] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Polynomial.CoeffList | {
"line": 105,
"column": 53
} | {
"line": 105,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nx : R\nhx : x ≠ 0\nn : ℕ\nh : ¬(monomial n) x = 0\nh₁✝ : 0 < ((monomial n) x).coeffList.length\nh₁ : 0 < (x :: List.replicate n 0).length\n⊢ ∀ (w : List R),\n ((monomial n) x).coeffList = ((monomial n) x).leadingCoeff :: w →\n ((monomial n) x).coeffList.get ⟨0,... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Polynomial.CoeffList | {
"line": 105,
"column": 53
} | {
"line": 105,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nx : R\nhx : x ≠ 0\nn : ℕ\nh : ¬(monomial n) x = 0\nh₁✝ : 0 < ((monomial n) x).coeffList.length\nh₁ : 0 < (x :: List.replicate n 0).length\n⊢ ∀ (w : List R),\n ((monomial n) x).coeffList = ((monomial n) x).leadingCoeff :: w →\n ((monomial n) x).coeffList.get ⟨0,... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.CoeffList | {
"line": 105,
"column": 53
} | {
"line": 105,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nx : R\nhx : x ≠ 0\nn : ℕ\nh : ¬(monomial n) x = 0\nh₁✝ : 0 < ((monomial n) x).coeffList.length\nh₁ : 0 < (x :: List.replicate n 0).length\n⊢ ∀ (w : List R),\n ((monomial n) x).coeffList = ((monomial n) x).leadingCoeff :: w →\n ((monomial n) x).coeffList.get ⟨0,... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Polynomial.CoeffList | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 12
} | [
{
"pp": "case neg.h.zero\nR : Type u_1\ninst✝ : Semiring R\nP : R[X]\nh✝ : P ≠ 0\nhdp : ¬P.natDegree = 0\nhep : ¬P.eraseLead = 0\nh₁ : P.degree.succ = P.natDegree + 1\nh₂ : P.eraseLead.degree.succ = P.eraseLead.natDegree + 1\nn : ℕ\nhn : P.natDegree = P.eraseLead.natDegree + 1 + n\nw : List R\nh : P.coeffList =... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 10
} | [
{
"pp": "case div\nK : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nn : ℤ\nd : ℕ\nhd : d ≠ 0\na✝ : n.natAbs.Coprime d\n⊢ mk (FiniteElement.mk (↑(↑n / ↑d) * ↑d) ⋯) = ↑(↑n / ↑d) * mk (FiniteElement.mk ↑d ⋯)",
"usedConstants": [
"Int.cast",
"ArchimedeanClass.FiniteEl... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 278,
"column": 15
} | {
"line": 278,
"column": 25
} | [
{
"pp": "K : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nx : K\nf : FiniteResidueField K →+*o ℝ\nh : 0 ≤ mk x\n⊢ (if h : 0 ≤ mk x then (Classical.ofNonempty.comp FiniteResidueField.mk) (FiniteElement.mk x h) else 0) =\n f (FiniteResidueField.mk (FiniteElement.mk x h))",
"... | dif_pos h, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 322,
"column": 32
} | {
"line": 322,
"column": 40
} | [
{
"pp": "K : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nx : K\nhx : mk x = 0\n⊢ 0 ≤ mk x⁻¹",
"usedConstants": [
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivis... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 323,
"column": 4
} | {
"line": 323,
"column": 35
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nx : K\nhx : mk x = 0\nhx' : 0 ≤ mk x⁻¹\n⊢ (if h : 0 ≤ mk x⁻¹ then (Classical.ofNonempty.comp FiniteResidueField.mk) (FiniteElement.mk x⁻¹ h) else 0) =\n (if h : 0 ≤ mk x then (Classical.ofNonempty.comp FiniteR... | rw [dif_pos hx.ge, dif_pos hx'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 38
} | [
{
"pp": "K : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nx y : K\nhx : 0 ≤ mk x\nhy : 0 ≤ mk y\n⊢ (if h : 0 ≤ mk (x + y) then (Classical.ofNonempty.comp FiniteResidueField.mk) (FiniteElement.mk (x + y) h) else 0) =\n (if h : 0 ≤ mk x then (Classical.ofNonempty.comp FiniteResi... | rw [dif_pos hx, dif_pos hy, dif_pos] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 360,
"column": 2
} | {
"line": 360,
"column": 38
} | [
{
"pp": "K : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nx y : K\nhx : 0 ≤ mk x\nhy : 0 ≤ mk y\n⊢ (if h : 0 ≤ mk (x * y) then (Classical.ofNonempty.comp FiniteResidueField.mk) (FiniteElement.mk (x * y) h) else 0) =\n (if h : 0 ≤ mk x then (Classical.ofNonempty.comp FiniteResi... | rw [dif_pos hx, dif_pos hy, dif_pos] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Ring.StandardPart | {
"line": 459,
"column": 6
} | {
"line": 459,
"column": 54
} | [
{
"pp": "case inl.hr\nK : Type u_1\ninst✝² : LinearOrder K\ninst✝¹ : Field K\ninst✝ : IsOrderedRing K\nf : ℝ →+*o K\nx : K\nhx : 0 ≤ mk x\na : ℤ\nha : ↑a < x\nb : ℤ\nhb✝ : x < ↑b\nhn : {r | x < f r}.Nonempty\nhb : BddBelow {r | x < f r}\nr : ℝ\nhr : r > sInf {r | x < f r}\n⊢ x ≤ f r",
"usedConstants": [
... | obtain ⟨s, hs, hs'⟩ := (csInf_lt_iff hb hn).1 hr | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.Derivation.MapCoeffs | {
"line": 45,
"column": 4
} | {
"line": 45,
"column": 12
} | [
{
"pp": "case add\nR : Type u_1\nA : Type u_2\nM : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Algebra R A\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : Module R M\nd : Derivation R A M\nq p✝ q✝ : A[X]\na✝¹ :\n (PolynomialModule.map A ↑d) (PolynomialModule.equivPolynomial.symm (p✝ * q... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.RingTheory.Derivation.MapCoeffs | {
"line": 48,
"column": 6
} | {
"line": 48,
"column": 14
} | [
{
"pp": "case monomial.add\nR : Type u_1\nA : Type u_2\nM : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Algebra R A\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : Module R M\nd : Derivation R A M\nn : ℕ\na : A\np✝ q✝ : A[X]\na✝¹ :\n (PolynomialModule.map A ↑d) (PolynomialModule.equivPo... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree | {
"line": 136,
"column": 2
} | {
"line": 141,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nhp : p.IsMonicOfDegree n\nhq : q.natDegree < n\n⊢ (p + q).IsMonicOfDegree n",
"usedConstants": [
"Nontrivial",
"Iff.mpr",
"Polynomial.coeff_add_eq_left_of_lt",
"Eq.mpr",
"Polynomial.IsMonicOfDegree.natDegree_eq",
... | rcases subsingleton_or_nontrivial R with H | H
· simpa using hp
refine (isMonicOfDegree_iff ..).mpr ⟨?_, ?_⟩
· exact natDegree_add_le_of_degree_le hp.natDegree_eq.le hq.le
· rw [coeff_add_eq_left_of_lt hq]
exact ((isMonicOfDegree_iff p n).mp hp).2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree | {
"line": 136,
"column": 2
} | {
"line": 141,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nhp : p.IsMonicOfDegree n\nhq : q.natDegree < n\n⊢ (p + q).IsMonicOfDegree n",
"usedConstants": [
"Nontrivial",
"Iff.mpr",
"Polynomial.coeff_add_eq_left_of_lt",
"Eq.mpr",
"Polynomial.IsMonicOfDegree.natDegree_eq",
... | rcases subsingleton_or_nontrivial R with H | H
· simpa using hp
refine (isMonicOfDegree_iff ..).mpr ⟨?_, ?_⟩
· exact natDegree_add_le_of_degree_le hp.natDegree_eq.le hq.le
· rw [coeff_add_eq_left_of_lt hq]
exact ((isMonicOfDegree_iff p n).mp hp).2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Derivation.MapCoeffs | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 10
} | [
{
"pp": "case add\nR : Type u_1\nA : Type u_2\nM : Type u_3\ninst✝¹² : CommRing R\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Algebra R A\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module A M\ninst✝⁷ : Module R M\nd : Derivation R A M\nB : Type u_4\nM' : Type u_5\ninst✝⁶ : CommRing B\ninst✝⁵ : Algebra R B\ninst✝⁴ : Algebra A B\ni... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 249,
"column": 2
} | {
"line": 250,
"column": 26
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\n⊢ R[X][Y] ≃ₐ[R] R[X][Y]",
"usedConstants": [
"Polynomial.C",
"Polynomial.eval",
"Algebra.algebraMap",
"Polynomial.ext",
"Polynomial.eval_C",
"congrArg",
"Comm... | apply AlgEquiv.ofAlgHom (aevalAeval (Y : R[X][Y]) (C X)) (aevalAeval (Y : R[X][Y]) (C X))
<;> (ext n m <;> simp) | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 249,
"column": 2
} | {
"line": 250,
"column": 26
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\n⊢ R[X][Y] ≃ₐ[R] R[X][Y]",
"usedConstants": [
"Polynomial.C",
"Polynomial.eval",
"Algebra.algebraMap",
"Polynomial.ext",
"Polynomial.eval_C",
"congrArg",
"Comm... | apply AlgEquiv.ofAlgHom (aevalAeval (Y : R[X][Y]) (C X)) (aevalAeval (Y : R[X][Y]) (C X))
<;> (ext n m <;> simp) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 249,
"column": 2
} | {
"line": 250,
"column": 26
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\n⊢ R[X][Y] ≃ₐ[R] R[X][Y]",
"usedConstants": [
"Polynomial.C",
"Polynomial.eval",
"Algebra.algebraMap",
"Polynomial.ext",
"Polynomial.eval_C",
"congrArg",
"Comm... | apply AlgEquiv.ofAlgHom (aevalAeval (Y : R[X][Y]) (C X)) (aevalAeval (Y : R[X][Y]) (C X))
<;> (ext n m <;> simp) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 273,
"column": 2
} | {
"line": 273,
"column": 10
} | [
{
"pp": "case add\nR : Type u_1\ninst✝ : CommSemiring R\np✝ q✝ : R[X]\na✝¹ : swap (map C p✝) = C p✝\na✝ : swap (map C q✝) = C q✝\n⊢ swap (map C (p✝ + q✝)) = C (p✝ + q✝)",
"usedConstants": [
"Polynomial.C",
"Polynomial.eval",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRin... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 10
} | [
{
"pp": "case add\nR : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nx y : A\np✝ q✝ : R[X][Y]\na✝¹ : (aevalAeval x y) (swap p✝) = (aevalAeval y x) p✝\na✝ : (aevalAeval x y) (swap q✝) = (aevalAeval y x) q✝\n⊢ (aevalAeval x y) (swap (p✝ + q✝)) = (aevalAeval y x) (p... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Polynomial.Bivariate | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 10
} | [
{
"pp": "case add\nR : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nx : A\np✝ q✝ : R[X][Y]\na✝¹ : (aeval (C x)) p✝ = (mapAlgHom (aeval x)) (swap p✝)\na✝ : (aeval (C x)) q✝ = (mapAlgHom (aeval x)) (swap q✝)\n⊢ (aeval (C x)) (p✝ + q✝) = (mapAlgHom (aeval x)) (swap... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Polynomial.DenomsClearable | {
"line": 51,
"column": 82
} | {
"line": 51,
"column": 91
} | [
{
"pp": "R : Type u_1\nK : Type u_2\ninst✝¹ : Semiring R\ninst✝ : CommSemiring K\ni : R →+* K\nb : R\nbi : K\nN : ℕ\na : R\nbu : bi * i b = 1\nn : ℕ\nr : R\nnN : n ≤ N\n⊢ i (r * a ^ n * b ^ (N - n)) = i b ^ N * (eval (i a * bi) (C (i r)) * eval (i a * bi) (X ^ n))",
"usedConstants": [
"Eq.mpr",
... | eval_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Polynomial.Mirror | {
"line": 49,
"column": 51
} | {
"line": 49,
"column": 61
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Semiring R\nn : ℕ\na : R\nha : ¬a = 0\n⊢ reflect (if a = 0 then 0 else n) ((monomial n) a) * X ^ ((monomial n) a).natTrailingDegree = (monomial n) a",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"HMul.hMul",
"congrArg",
"LinearMap.... | if_neg ha, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Destutter | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 34
} | [
{
"pp": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na : α\nh : destutter' R a l = a :: l\n⊢ IsChain R (destutter' R a l)",
"usedConstants": [
"List.isChain_destutter'"
]
}
] | exact l.isChain_destutter' R a | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Polynomial.PartialFractions | {
"line": 132,
"column": 4
} | {
"line": 133,
"column": 58
} | [
{
"pp": "case succ.snoc.snoc\nR : Type u_1\ninst✝ : CommRing R\ng : R[X]\nhg : g.Monic\nn : ℕ\nih :\n ∀ {q₁ q₂ : R[X]} {r₁ r₂ : Fin n → R[X]},\n (∀ (i : Fin n), (r₁ i).degree < g.degree) →\n (∀ (i : Fin n), (r₂ i).degree < g.degree) →\n q₁ * g ^ n + ∑ i, r₁ i * g ^ ↑i = q₂ * g ^ n + ∑ i, r₂ i * ... | simp only [Fin.sum_univ_castSucc, Fin.snoc_castSucc,
Fin.val_castSucc, Fin.snoc_last, Fin.val_last] at hf | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Polynomial.SpecificDegree | {
"line": 29,
"column": 41
} | {
"line": 29,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nhp : Monic 1\nhp2 : 2 ≤ natDegree 1\nhp3 : natDegree 1 ≤ 3\nhp0 : 1 ≠ 0\n⊢ False",
"usedConstants": [
"Polynomial.instOne",
"congrArg",
"CommSemiring.toSemiring",
"Eq.mp",
"instOfNatNat",
"LE.le",
"inst... | natDegree_one | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Polynomial.Smeval | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 34
} | [
{
"pp": "R : Type u_3\ninst✝³ : Semiring R\nS : Type u_4\ninst✝² : Semiring S\ninst✝¹ : Module R S\ninst✝ : IsScalarTower R S S\np : R[X]\nx : S\n⊢ eval₂ RingHom.smulOneHom x p = p.smeval x",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Polynomial.sum",
"Module.toMulA... | rw [smeval_eq_sum, eval₂_eq_sum] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Polynomial.SpecificDegree | {
"line": 65,
"column": 4
} | {
"line": 65,
"column": 12
} | [
{
"pp": "case pos.a\nK : Type u_1\ninst✝ : Field K\np : K[X]\nhdeg : 1 ≤ p.natDegree ∧ p.natDegree ≤ 3\nhnot : ∀ (x : K), ¬p.IsRoot x\nhdeg2 : 2 ≤ p.natDegree\n⊢ ∀ (x : K), x ∉ p.roots",
"usedConstants": [
"Polynomial.eval",
"False",
"Polynomial.roots",
"eq_false",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Polynomial.PartialFractions | {
"line": 215,
"column": 8
} | {
"line": 218,
"column": 95
} | [
{
"pp": "case cons\nR : Type u_1\ninst✝¹ : CommRing R\nι : Type u_2\ninst✝ : DecidableEq ι\ng : ι → R[X]\ni j : ι\ns : Finset ι\nhj : j ∉ s\nih : ∀ (hi : i ∉ s), ((↑(Finset.cons i s hi)).Pairwise fun i j ↦ IsCoprime (g i) (g j)) → IsCoprime (g i) (∏ i ∈ s, g i)\nhi : i ∉ Finset.cons j s hj\nhgg : (↑(Finset.cons... | rw [Finset.prod_cons, IsCoprime.mul_right_iff]
refine ⟨hgg (by simp) (by simp) fun hij => hi (by simp [hij]), ih ?_ ?_⟩
· exact mt Finset.mem_cons_of_mem hi
· exact hgg.mono (SetLike.coe_mono (Finset.cons_subset_cons.2 (Finset.subset_cons hj))) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.PartialFractions | {
"line": 215,
"column": 8
} | {
"line": 218,
"column": 95
} | [
{
"pp": "case cons\nR : Type u_1\ninst✝¹ : CommRing R\nι : Type u_2\ninst✝ : DecidableEq ι\ng : ι → R[X]\ni j : ι\ns : Finset ι\nhj : j ∉ s\nih : ∀ (hi : i ∉ s), ((↑(Finset.cons i s hi)).Pairwise fun i j ↦ IsCoprime (g i) (g j)) → IsCoprime (g i) (∏ i ∈ s, g i)\nhi : i ∉ Finset.cons j s hj\nhgg : (↑(Finset.cons... | rw [Finset.prod_cons, IsCoprime.mul_right_iff]
refine ⟨hgg (by simp) (by simp) fun hij => hi (by simp [hij]), ih ?_ ?_⟩
· exact mt Finset.mem_cons_of_mem hi
· exact hgg.mono (SetLike.coe_mono (Finset.cons_subset_cons.2 (Finset.subset_cons hj))) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Polynomial.Smeval | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 32
} | [
{
"pp": "case h\nR : Type u_3\ninst✝ : Semiring R\nr : R\nx✝ : R[X]\n⊢ (leval r) x✝ = x✝.smeval r",
"usedConstants": [
"MonoidWithZero.toMulActionWithZero",
"Semiring.toModule",
"LinearMap.instFunLike",
"id",
"Polynomial.leval",
"LinearMap",
"Polynomial",
"Mon... | simpa using eval_eq_smeval _ _ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Polynomial.UnitTrinomial | {
"line": 94,
"column": 48
} | {
"line": 95,
"column": 85
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\nhw : w ≠ 0\n⊢ (trinomial k m n u v w).leadingCoeff = w",
"usedConstants": [
"Eq.mpr",
"Polynomial.leadingCoeff.eq_1",
"Polynomial.trinomial",
"congrArg",
"Polynomial.trinomial_leading_coe... | by
rw [leadingCoeff, trinomial_natDegree hkm hmn hw, trinomial_leading_coeff' hkm hmn] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Polynomial.UnitTrinomial | {
"line": 186,
"column": 8
} | {
"line": 186,
"column": 16
} | [
{
"pp": "case refine_1\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nu v w : ℤˣ\n⊢ ((trinomial k m n ↑u ↑v ↑w).sum fun x x_1 ↦ x_1 ^ 2) = 3",
"usedConstants": [
"Units.val",
"Eq.mpr",
"Polynomial.trinomial",
"congrArg",
"Polynomial.sum",
"id",
"instOfNatNat",
"Int",
... | sum_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Polynomial.UnitTrinomial | {
"line": 196,
"column": 8
} | {
"line": 196,
"column": 16
} | [
{
"pp": "case refine_2\np : ℤ[X]\nhp : (p.sum fun x x_1 ↦ x_1 ^ 2) = 3\nkey : ∀ k ∈ p.support, p.coeff k ^ 2 = 1\n⊢ #p.support = 3",
"usedConstants": [
"congrArg",
"Polynomial.sum",
"Eq.mp",
"instOfNatNat",
"Int",
"Polynomial.coeff",
"Monoid.toPow",
"NonUnital... | sum_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Polynomial.UnitTrinomial | {
"line": 273,
"column": 39
} | {
"line": 273,
"column": 61
} | [
{
"pp": "case inr\np q : ℤ[X]\nk m m' n : ℕ\nhkm : k < m\nhmn : m < n\nhkm' : k < m'\nhmn' : m' < n\nu v w : ℤˣ\nhp : p = trinomial k m n ↑u ↑v ↑w\nh : p * p.mirror = q.mirror.mirror.mirror * q.mirror.mirror\nhq : q.mirror = trinomial k (n - m' + k) n ↑u ↑v ↑w\nhmul : ↑w * ↑u = ↑u * ↑w\n⊢ q = p ∨ q = p.mirror",... | q.mirror.mirror_mirror | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.QuadraticAlgebra.Defs | {
"line": 131,
"column": 78
} | {
"line": 132,
"column": 21
} | [
{
"pp": "R : Type u_1\na b : R\ninst✝¹ : Zero R\ninst✝ : One R\nr : R\n⊢ QuadraticAlgebra.C r = 1 ↔ r = 1",
"usedConstants": [
"Eq.mpr",
"QuadraticAlgebra",
"congrArg",
"QuadraticAlgebra.C",
"Iff.rfl",
"id",
"Iff",
"QuadraticAlgebra.C_one",
"QuadraticAlg... | by
rw [← C_one, C_inj] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : SignType.sign P.leadingCoeff = SignType.sign P.nextCoeff\nhpz : P = 0\n⊢ P.eraseLead.signVariations = P.signVariations",
"usedConstants": [
"Polynomial.signVariations",
"congrArg",
"Polynomial.signVa... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : SignType.sign P.leadingCoeff = SignType.sign P.nextCoeff\nhpz : P = 0\n⊢ P.eraseLead.signVariations = P.signVariations",
"usedConstants": [
"Polynomial.signVariations",
"congrArg",
"Polynomial.signVa... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : SignType.sign P.leadingCoeff = SignType.sign P.nextCoeff\nhpz : P = 0\n⊢ P.eraseLead.signVariations = P.signVariations",
"usedConstants": [
"Polynomial.signVariations",
"congrArg",
"Polynomial.signVa... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 72,
"column": 43
} | {
"line": 72,
"column": 51
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : SignType.sign P.leadingCoeff = SignType.sign P.nextCoeff\nhpz : ¬P = 0\na✝ : P.nextCoeff = 0\n⊢ False",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"sign_eq_zero_iff._simp_1",
"False.elim",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : P ≠ 0\nhpz : P = 0\n⊢ P.signVariations =\n P.eraseLead.signVariations + if SignType.sign P.leadingCoeff = -SignType.sign P.eraseLead.leadingCoeff then 1 else 0",
"usedConstants": [
"False",
"Polynomial.... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : P ≠ 0\nhpz : P = 0\n⊢ P.signVariations =\n P.eraseLead.signVariations + if SignType.sign P.leadingCoeff = -SignType.sign P.eraseLead.leadingCoeff then 1 else 0",
"usedConstants": [
"False",
"Polynomial.... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : P ≠ 0\nhpz : P = 0\n⊢ P.signVariations =\n P.eraseLead.signVariations + if SignType.sign P.leadingCoeff = -SignType.sign P.eraseLead.leadingCoeff then 1 else 0",
"usedConstants": [
"False",
"Polynomial.... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Polynomial.RuleOfSigns | {
"line": 84,
"column": 54
} | {
"line": 84,
"column": 62
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : LinearOrder R\nP : R[X]\nh : P ≠ 0\nhpz : ¬P = 0\n⊢ SignType.sign P.leadingCoeff ≠ 0",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"sign_eq_zero_iff._simp_1",
"PartialOrder.toPreorder",
"SignType.instLinearOrder"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Quandle | {
"line": 661,
"column": 8
} | {
"line": 661,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Rack R\nG : Type u_2\ninst✝ : Group G\nf : R →◃ Quandle.Conj G\n⊢ ⟦unit⟧.liftOn (mapAux f) ⋯ = 1",
"usedConstants": [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"eq_self",
... | simp only [Quotient.lift_mk, mapAux] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.QuaternionBasis | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 72
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nc₁ c₂ c₃ : R\nq : Basis A c₁ c₂ c₃\nx y : ℍ[R,c₁,c₂,c₃]\n⊢ q.lift (x + y) = q.lift x + q.lift y",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClas... | simp only [lift, re_add, map_add, imI_add, add_smul, imJ_add, imK_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 14
} | [
{
"pp": "case sq_add.inl\nR : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\ns✝ s : R\nhs✝ : IsSumSq s\nih : s ≠ 0 → IsSumNonzeroSq s\nhs : 0 * 0 + s ≠ 0\n⊢ IsSumNonzeroSq (0 * 0 + s)",
"usedConstants": [
"IsSumNonzeroSq",
"False",
"HMul.hMul",
"eq_false",
"congrArg",
"Ad... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 14
} | [
{
"pp": "case sq_add.inl\nR : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\ns✝ s : R\nhs✝ : IsSumSq s\nih : s ≠ 0 → IsSumNonzeroSq s\nhs : 0 * 0 + s ≠ 0\n⊢ IsSumNonzeroSq (0 * 0 + s)",
"usedConstants": [
"IsSumNonzeroSq",
"False",
"HMul.hMul",
"eq_false",
"congrArg",
"Ad... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 14
} | [
{
"pp": "case sq_add.inl\nR : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\ns✝ s : R\nhs✝ : IsSumSq s\nih : s ≠ 0 → IsSumNonzeroSq s\nhs : 0 * 0 + s ≠ 0\n⊢ IsSumNonzeroSq (0 * 0 + s)",
"usedConstants": [
"IsSumNonzeroSq",
"False",
"HMul.hMul",
"eq_false",
"congrArg",
"Ad... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 141,
"column": 34
} | {
"line": 141,
"column": 42
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : IsFormallyReal R\ns₁ s₂ : R\nhs₁ : IsSumSq s₁\nhs₂ : IsSumSq s₂\nh : s₁ + s₂ = 0\nh₁ : s₁ ≠ 0\nhc : s₂ = 0\n⊢ False",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 141,
"column": 34
} | {
"line": 141,
"column": 42
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : IsFormallyReal R\ns₁ s₂ : R\nhs₁ : IsSumSq s₁\nhs₂ : IsSumSq s₂\nh : s₁ + s₂ = 0\nh₁ : s₁ ≠ 0\nhc : s₂ = 0\n⊢ False",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.IsFormallyReal | {
"line": 141,
"column": 34
} | {
"line": 141,
"column": 42
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : IsFormallyReal R\ns₁ s₂ : R\nhs₁ : IsSumSq s₁\nhs₂ : IsSumSq s₂\nh : s₁ + s₂ = 0\nh₁ : s₁ ≠ 0\nhc : s₂ = 0\n⊢ False",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.SkewMonoidAlgebra.Lift | {
"line": 233,
"column": 24
} | {
"line": 233,
"column": 32
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁶ : Semiring k\ninst✝⁵ : Monoid G\ninst✝⁴ : MulSemiringAction G k\nV : Type u_4\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\ninst✝¹ : Module (SkewMonoidAlgebra k G) V\ninst✝ : IsScalarTower k (SkewMonoidAlgebra k G) V\nW : Submodule k V\nh : ∀ (g : G), ... | sum_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Star.CHSH | {
"line": 182,
"column": 4
} | {
"line": 182,
"column": 90
} | [
{
"pp": "R : Type u\ninst✝⁶ : Ring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : StarRing R\ninst✝³ : StarOrderedRing R\ninst✝² : Algebra ℝ R\ninst✝¹ : IsOrderedModule ℝ R\ninst✝ : StarModule ℝ R\nA₀ A₁ B₀ B₁ : R\nT : IsCHSHTuple A₀ A₁ B₀ B₁\nM : ∀ (m : ℤ) (a : ℝ) (x : R), m • a • x = (↑m * a) • x\nP : R := (√2)⁻¹ • (A₁... | simp only [← T.A₀B₀_commutes, ← T.A₀B₁_commutes, ← T.A₁B₀_commutes, ← T.A₁B₁_commutes] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Star.RingQuot | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 20
} | [
{
"pp": "R✝ : Type u\ninst✝³ : Semiring R✝\nr✝ : R✝ → R✝ → Prop\ninst✝² : StarRing R✝\nR : Type u\ninst✝¹ : Semiring R\ninst✝ : StarRing R\nr : R → R → Prop\nhr : ∀ (a b : R), r a b → r (star a) (star b)\n⊢ ∀ (r_1 s : RingQuot r), star' r hr (r_1 * s) = star' r hr s * star' r hr r_1",
"usedConstants": [
... | rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Algebra.Star.RingQuot | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 20
} | [
{
"pp": "R✝ : Type u\ninst✝³ : Semiring R✝\nr✝ : R✝ → R✝ → Prop\ninst✝² : StarRing R✝\nR : Type u\ninst✝¹ : Semiring R\ninst✝ : StarRing R\nr : R → R → Prop\nhr : ∀ (a b : R), r a b → r (star a) (star b)\n⊢ ∀ (r_1 s : RingQuot r), star' r hr (r_1 + s) = star' r hr r_1 + star' r hr s",
"usedConstants": [
... | rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 79,
"column": 20
} | {
"line": 79,
"column": 59
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝¹ : AddMonoid k\nS : Type u_3\ninst✝ : SMulZeroClass S k\na : S\n⊢ a • 0 = 0",
"usedConstants": [
"Finsupp.smulZeroClass",
"instHSMul",
"AddMonoid.toAddZeroClass",
"smul_zero",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.ofFinsup... | exact congr_arg ofFinsupp (smul_zero a) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 79,
"column": 20
} | {
"line": 79,
"column": 59
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝¹ : AddMonoid k\nS : Type u_3\ninst✝ : SMulZeroClass S k\na : S\n⊢ a • 0 = 0",
"usedConstants": [
"Finsupp.smulZeroClass",
"instHSMul",
"AddMonoid.toAddZeroClass",
"smul_zero",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.ofFinsup... | exact congr_arg ofFinsupp (smul_zero a) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 79,
"column": 20
} | {
"line": 79,
"column": 59
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝¹ : AddMonoid k\nS : Type u_3\ninst✝ : SMulZeroClass S k\na : S\n⊢ a • 0 = 0",
"usedConstants": [
"Finsupp.smulZeroClass",
"instHSMul",
"AddMonoid.toAddZeroClass",
"smul_zero",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.ofFinsup... | exact congr_arg ofFinsupp (smul_zero a) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 335,
"column": 18
} | {
"line": 335,
"column": 26
} | [
{
"pp": "case zero\nk : Type u_1\nG : Type u_2\ninst✝¹ : One G\ninst✝ : AddMonoidWithOne k\n⊢ ↑0 = single 1 ↑0",
"usedConstants": [
"congrArg",
"AddMonoid.toAddZeroClass",
"SkewMonoidAlgebra.instZero",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.single_zero",
"AddMonoidW... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 335,
"column": 18
} | {
"line": 335,
"column": 26
} | [
{
"pp": "case succ\nk : Type u_1\nG : Type u_2\ninst✝¹ : One G\ninst✝ : AddMonoidWithOne k\nn✝ : ℕ\na✝ : ↑n✝ = single 1 ↑n✝\n⊢ ↑(n✝ + 1) = single 1 ↑(n✝ + 1)",
"usedConstants": [
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddM... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 427,
"column": 6
} | {
"line": 427,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\nM : Type u_5\nN : Type u_6\nP : Type u_7\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\ninst✝ : AddCommMonoid P\nf : SkewMonoidAlgebra M α\ng : α → M → SkewMonoidAlgebra N β\nh : β → N → P\nh_zero : ∀ (a : β), h a 0 = 0\nh_add : ∀ (a : β) (b₁ b₂ : N), h a (b₁ + b₂) = h... | sum_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 433,
"column": 34
} | {
"line": 433,
"column": 42
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝¹ : AddCommMonoid k\nk' : Type u_3\nG' : Type u_4\ninst✝ : AddCommMonoid k'\nf : SkewMonoidAlgebra k G\ng : G → k → SkewMonoidAlgebra k' G'\na₂ : G'\n⊢ (f.toFinsupp.sum fun x1 x2 ↦ (g x1 x2).toFinsupp) a₂ = f.sum fun a₁ b ↦ (g a₁ b).toFinsupp a₂",
"usedConstants": [... | sum_def, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 464,
"column": 46
} | {
"line": 464,
"column": 54
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝ : AddCommMonoid k\np : SkewMonoidAlgebra k G → Prop\nf : SkewMonoidAlgebra k G\nzero : p 0\nsingle : ∀ (g : G) (a : k), p (SkewMonoidAlgebra.single g a)\nadd : ∀ (f g : SkewMonoidAlgebra k G), p f → p g → p (f + g)\n⊢ ∀ x ∈ f.support, p (SkewMonoidAlgebra.single x (f.c... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 464,
"column": 46
} | {
"line": 464,
"column": 54
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝ : AddCommMonoid k\np : SkewMonoidAlgebra k G → Prop\nf : SkewMonoidAlgebra k G\nzero : p 0\nsingle : ∀ (g : G) (a : k), p (SkewMonoidAlgebra.single g a)\nadd : ∀ (f g : SkewMonoidAlgebra k G), p f → p g → p (f + g)\n⊢ ∀ x ∈ f.support, p (SkewMonoidAlgebra.single x (f.c... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 464,
"column": 46
} | {
"line": 464,
"column": 54
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝ : AddCommMonoid k\np : SkewMonoidAlgebra k G → Prop\nf : SkewMonoidAlgebra k G\nzero : p 0\nsingle : ∀ (g : G) (a : k), p (SkewMonoidAlgebra.single g a)\nadd : ∀ (f g : SkewMonoidAlgebra k G), p f → p g → p (f + g)\n⊢ ∀ x ∈ f.support, p (SkewMonoidAlgebra.single x (f.c... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 478,
"column": 62
} | {
"line": 478,
"column": 70
} | [
{
"pp": "case h.zero\nk : Type u_1\nG : Type u_2\ninst✝¹ : AddCommMonoid k\nM : Type u_3\ninst✝ : AddZeroClass M\nf g : SkewMonoidAlgebra k G →+ M\nh : ∀ (a : G) (b : k), f (single a b) = g (single a b)\n⊢ f 0 = g 0",
"usedConstants": [
"AddMonoidHom.instAddMonoidHomClass",
"congrArg",
"Ad... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 478,
"column": 62
} | {
"line": 478,
"column": 70
} | [
{
"pp": "case h.single\nk : Type u_1\nG : Type u_2\ninst✝¹ : AddCommMonoid k\nM : Type u_3\ninst✝ : AddZeroClass M\nf g : SkewMonoidAlgebra k G →+ M\nh : ∀ (a : G) (b : k), f (single a b) = g (single a b)\ng✝ : G\na✝ : k\n⊢ f (single g✝ a✝) = g (single g✝ a✝)",
"usedConstants": [
"congrArg",
"Ad... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 478,
"column": 62
} | {
"line": 478,
"column": 70
} | [
{
"pp": "case h.add\nk : Type u_1\nG : Type u_2\ninst✝¹ : AddCommMonoid k\nM : Type u_3\ninst✝ : AddZeroClass M\nf g : SkewMonoidAlgebra k G →+ M\nh : ∀ (a : G) (b : k), f (single a b) = g (single a b)\nf✝ g✝ : SkewMonoidAlgebra k G\na✝¹ : f f✝ = g f✝\na✝ : f g✝ = g g✝\n⊢ f (f✝ + g✝) = g (f✝ + g✝)",
"usedCo... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 500,
"column": 67
} | {
"line": 501,
"column": 70
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝ : AddCommMonoid k\nG' : Type u_3\nf : G → G'\nv : SkewMonoidAlgebra k G\n⊢ ((mapDomain f) v).toFinsupp = Finsupp.mapDomain f v.toFinsupp",
"usedConstants": [
"Eq.mpr",
"SkewMonoidAlgebra.mapDomain",
"congrArg",
"Finsupp.mapDomain",
"Ad... | by
simp_rw [mapDomain_apply, Finsupp.mapDomain, toFinsupp_sum', single] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 546,
"column": 11
} | {
"line": 546,
"column": 19
} | [
{
"pp": "case h\nk : Type u_1\nG : Type u_2\ninst✝¹ : AddCommMonoid k\nR : Type u_5\ninst✝ : NonUnitalNonAssocSemiring R\nf : k →+ R\ng : G → R\nl : SkewMonoidAlgebra k G →+ R\nh : ∀ (a : G) (b : k), l (single a b) = f b * g a\na : G\nb : k\n⊢ l (single a b) = (liftNC f g) (single a b)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 697,
"column": 8
} | {
"line": 697,
"column": 16
} | [
{
"pp": "case single.single.add\nk : Type u_1\nG : Type u_2\ninst✝² : Semiring k\ninst✝¹ : Monoid G\ninst✝ : MulSemiringAction G k\nx : G\na : k\ny : G\nb : k\nf✝ g✝ : SkewMonoidAlgebra k G\na✝¹ : single x a * single y b * f✝ = single x a * (single y b * f✝)\na✝ : single x a * single y b * g✝ = single x a * (si... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.SkewMonoidAlgebra.Basic | {
"line": 698,
"column": 6
} | {
"line": 698,
"column": 14
} | [
{
"pp": "case single.add\nk : Type u_1\nG : Type u_2\ninst✝² : Semiring k\ninst✝¹ : Monoid G\ninst✝ : MulSemiringAction G k\nh : SkewMonoidAlgebra k G\nx : G\na : k\nf✝ g✝ : SkewMonoidAlgebra k G\na✝¹ : single x a * f✝ * h = single x a * (f✝ * h)\na✝ : single x a * g✝ * h = single x a * (g✝ * h)\n⊢ single x a *... | | add => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
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