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.BigOperators.Finprod | {
"line": 626,
"column": 6
} | {
"line": 626,
"column": 28
} | [
{
"pp": "M : Type u_7\nα : Type u_8\ninst✝³ : CommMonoidWithZero M\ninst✝² : PartialOrder M\ninst✝¹ : ZeroLEOneClass M\ninst✝ : PosMulMono M\n⊢ ∏ᶠ (x : α), 0 ≤ 1",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg"... | ← finprod_one (α := α) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Finsupp.LinearCombination | {
"line": 324,
"column": 61
} | {
"line": 324,
"column": 70
} | [
{
"pp": "α : Type u_1\nM : Type u_2\nR : Type u_3\ninst✝⁴ : Fintype α\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\nv : α → M\ninst✝ : DecidableEq α\ni : α\nr : R\n⊢ ∑ x, (if x = i then r else 0) • v x = r • v i",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"Finset.uni... | ite_smul, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.LinearAlgebra.Basis.Defs | {
"line": 448,
"column": 4
} | {
"line": 448,
"column": 76
} | [
{
"pp": "case h\nι : Type u_10\nR : Type u_11\nM : Type u_12\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\nx : M\ni✝ : ι\na✝ : Nontrivial R\ni j : ι\n⊢ (single ⟨b i, ⋯⟩ 1) ⟨b j, ⋯⟩ = (single i 1) j",
"usedConstants": [
"Set.mem_range_self",
"NonAssocSemirin... | apply Finsupp.single_apply_left (f := fun i => (⟨b i, _⟩ : Set.range b)) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1051,
"column": 2
} | {
"line": 1051,
"column": 78
} | [
{
"pp": "α : Type u_1\nι : Type u_3\nM : Type u_5\ninst✝ : CommMonoid M\nf : α → M\nI : Set ι\nt : ι → Set α\nh : I.PairwiseDisjoint t\nhI : I.Finite\nht : ∀ i ∈ I, (t i).Finite\nthis : Fintype ↑I\n⊢ ∏ᶠ (a : α) (_ : a ∈ ⋃ x ∈ I, t x), f a = ∏ᶠ (i : ι) (_ : i ∈ I) (j : α) (_ : j ∈ t i), f j",
"usedConstants"... | rw [biUnion_eq_iUnion, finprod_mem_iUnion, ← finprod_set_coe_eq_finprod_mem] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1223,
"column": 4
} | {
"line": 1223,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ r * ∑ᶠ (a : α), f a = ∑ᶠ (a : α), r * f a",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"MulZeroClass.zero_mul",
"finsum... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1223,
"column": 4
} | {
"line": 1223,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ r * ∑ᶠ (a : α), f a = ∑ᶠ (a : α), r * f a",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"MulZeroClass.zero_mul",
"finsum... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1223,
"column": 4
} | {
"line": 1223,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ r * ∑ᶠ (a : α), f a = ∑ᶠ (a : α), r * f a",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"MulZeroClass.zero_mul",
"finsum... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1238,
"column": 25
} | {
"line": 1238,
"column": 33
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\ns : Set α\nf : α → R\nr : R\na : α\nh : a ∈ s\n⊢ r * ∑ᶠ (_ : a ∈ s), f a = ∑ᶠ (_ : a ∈ s), r * f a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"finsum",
"Membership.mem",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1238,
"column": 25
} | {
"line": 1238,
"column": 33
} | [
{
"pp": "case neg\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\ns : Set α\nf : α → R\nr : R\na : α\nh : a ∉ s\n⊢ r * ∑ᶠ (_ : a ∈ s), f a = ∑ᶠ (_ : a ∈ s), r * f a",
"usedConstants": [
"False",
"HMul.hMul",
"eq_false",
"congrArg",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1249,
"column": 4
} | {
"line": 1249,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ (∑ᶠ (a : α), f a) * r = ∑ᶠ (a : α), f a * r",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"finsum",
"AddMonoid.toAddZero... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1249,
"column": 4
} | {
"line": 1249,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ (∑ᶠ (a : α), f a) * r = ∑ᶠ (a : α), f a * r",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"finsum",
"AddMonoid.toAddZero... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1249,
"column": 4
} | {
"line": 1249,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nf : α → R\nr : R\nhr : r = 0\n⊢ (∑ᶠ (a : α), f a) * r = ∑ᶠ (a : α), f a * r",
"usedConstants": [
"finsum_zero",
"HMul.hMul",
"congrArg",
"finsum",
"AddMonoid.toAddZero... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Basis.Defs | {
"line": 697,
"column": 2
} | {
"line": 697,
"column": 66
} | [
{
"pp": "ι : Type u_10\nR : Type u_11\nM : Type u_12\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\ni : ι\nf : ι →₀ R\n⊢ (b.coord i) (b.repr.symm f) = f i",
"usedConstants": [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsu... | simp only [repr_symm_apply, coord_apply, repr_linearCombination] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Basis.Defs | {
"line": 697,
"column": 2
} | {
"line": 697,
"column": 66
} | [
{
"pp": "ι : Type u_10\nR : Type u_11\nM : Type u_12\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\ni : ι\nf : ι →₀ R\n⊢ (b.coord i) (b.repr.symm f) = f i",
"usedConstants": [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsu... | simp only [repr_symm_apply, coord_apply, repr_linearCombination] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Basis.Defs | {
"line": 697,
"column": 2
} | {
"line": 697,
"column": 66
} | [
{
"pp": "ι : Type u_10\nR : Type u_11\nM : Type u_12\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\ni : ι\nf : ι →₀ R\n⊢ (b.coord i) (b.repr.symm f) = f i",
"usedConstants": [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsu... | simp only [repr_symm_apply, coord_apply, repr_linearCombination] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1264,
"column": 25
} | {
"line": 1264,
"column": 33
} | [
{
"pp": "case pos\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\ns : Set α\nf : α → R\nr : R\na : α\nh : a ∈ s\n⊢ (∑ᶠ (_ : a ∈ s), f a) * r = ∑ᶠ (_ : a ∈ s), f a * r",
"usedConstants": [
"HMul.hMul",
"congrArg",
"finsum",
"Membership.mem"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1264,
"column": 25
} | {
"line": 1264,
"column": 33
} | [
{
"pp": "case neg\nα : Type u_1\nR : Type u_7\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\ns : Set α\nf : α → R\nr : R\na : α\nh : a ∉ s\n⊢ (∑ᶠ (_ : a ∈ s), f a) * r = ∑ᶠ (_ : a ∈ s), f a * r",
"usedConstants": [
"False",
"HMul.hMul",
"eq_false",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1299,
"column": 2
} | {
"line": 1299,
"column": 33
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝² : CommMonoid M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Finset (α × β)\nf : α × β → M\nthis : ∀ (a : α), ∏ i ∈ Finset.image Prod.snd ({ab ∈ s | ab.1 = a}), f (a, i) = {x ∈ s | x.1 = a}.prod f\n⊢ ∏ᶠ (ab : α × β) (_ : ab ∈ s), f ab =\n ∏ᶠ (a ... | rw [finprod_mem_finset_eq_prod] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.BigOperators.Finprod | {
"line": 1329,
"column": 11
} | {
"line": 1329,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nM : Type u_5\ninst✝ : CommMonoid M\nf : α × β → M\nhf : HasFiniteMulSupport f\nh₁ : ∀ (a : α × β), ∏ᶠ (_ : a ∈ Finite.toFinset hf), f a = f a\nh₂ : ∏ᶠ (a : α × β), f a = ∏ᶠ (a : α × β) (_ : a ∈ Finite.toFinset hf), f a\n⊢ ∏ᶠ (ab : α × β), f ab = ∏ᶠ (a : α) (b : β), f (a, b)"... | h₂, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Fintype.Fin | {
"line": 80,
"column": 43
} | {
"line": 80,
"column": 73
} | [
{
"pp": "n : ℕ\nj : Fin n\np : Fin n → Prop\ninst✝ : DecidablePred p\nhp : ∀ (i j : Fin n), j ≤ i → p i → p j\nh1 : ∀ (k : Fin n), ¬p k → #{i | p i} ≤ ↑k\nh : p j\nhc : #{i | p i} ≤ ↑j\nq : Fin n → Prop := fun x ↦ ↑x < #{i | p i}\n⊢ #(filter p univ) ≤ #(filter q univ)",
"usedConstants": [
"Eq.mpr",
... | rw [card_filter_val_lt]; grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.Fin | {
"line": 80,
"column": 43
} | {
"line": 80,
"column": 73
} | [
{
"pp": "n : ℕ\nj : Fin n\np : Fin n → Prop\ninst✝ : DecidablePred p\nhp : ∀ (i j : Fin n), j ≤ i → p i → p j\nh1 : ∀ (k : Fin n), ¬p k → #{i | p i} ≤ ↑k\nh : p j\nhc : #{i | p i} ≤ ↑j\nq : Fin n → Prop := fun x ↦ ↑x < #{i | p i}\n⊢ #(filter p univ) ≤ #(filter q univ)",
"usedConstants": [
"Eq.mpr",
... | rw [card_filter_val_lt]; grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.ModEq | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 29
} | [
{
"pp": "M : Type u_1\ninst✝ : AddCommMonoid M\na b c p : M\nhab : ∃ m n, m • p + a = n • p + b\nhbc : ∃ m n, m • p + b = n • p + c\n⊢ ∃ m n, m • p + a = n • p + c",
"usedConstants": []
}
] | rcases hab with ⟨m, n, hab⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Data.Nat.GCD.Basic | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 12
} | [
{
"pp": "case inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.instMonoid",
"Nat.zero_div",
"Se... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.GCD.Basic | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 12
} | [
{
"pp": "case inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.instMonoid",
"Nat.zero_div",
"Se... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.GCD.Basic | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 12
} | [
{
"pp": "case inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.instMonoid",
"Nat.zero_div",
"Se... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.GCD.Basic | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 12
} | [
{
"pp": "case inr.inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m > 0\nhn : n = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.gcd_zero_right",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.GCD.Basic | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 12
} | [
{
"pp": "case inr.inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m > 0\nhn : n = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.gcd_zero_right",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.GCD.Basic | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 12
} | [
{
"pp": "case inr.inl\nn m k : ℕ\nhkm : m ∣ k\nhkn : n ∣ k\nc : ℕ\nhmc : k / m ∣ c\nhnc : k / n ∣ c\nhm : m > 0\nhn : n = 0\n⊢ k / m.gcd n ∣ c",
"usedConstants": [
"Nat.gcd",
"Dvd.dvd",
"instHDiv",
"Nat.gcd_zero_right",
"Nat.instSemigroupWithZero",
"congrArg",
"Nat.... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.LinearIndependent.Basic | {
"line": 462,
"column": 74
} | {
"line": 462,
"column": 90
} | [
{
"pp": "ι : Type u'\nR : Type u_2\ns : Set ι\nM : Type u_4\nv : ι → M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nt : Set ι\nhs : LinearIndepOn R v s\nht : LinearIndepOn R v t\nhdj : Disjoint (span R (v '' s)) (span R (v '' t))\na✝ : Nontrivial R\n⊢ Disjoint (span R (v '' s)) (span R (range ... | ← image_eq_range | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.LinearIndependent.Basic | {
"line": 462,
"column": 2
} | {
"line": 462,
"column": 92
} | [
{
"pp": "ι : Type u'\nR : Type u_2\ns : Set ι\nM : Type u_4\nv : ι → M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nt : Set ι\nhs : LinearIndepOn R v s\nht : LinearIndepOn R v t\nhdj : Disjoint (span R (v '' s)) (span R (v '' t))\na✝ : Nontrivial R\n⊢ LinearIndepOn R v (s ∪ t)",
"usedConst... | have hli := LinearIndependent.sum_type hs ht (by rwa [← image_eq_range, ← image_eq_range]) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.Nat.ModEq | {
"line": 568,
"column": 53
} | {
"line": 568,
"column": 61
} | [
{
"pp": "m n : ℕ\nhm1 : m % 2 = 1\nhn1 : n % 2 = 1\nh : n = 0\n⊢ False",
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"zero_ne_one._simp_1",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.ModEq | {
"line": 568,
"column": 53
} | {
"line": 568,
"column": 61
} | [
{
"pp": "m n : ℕ\nhm1 : m % 2 = 1\nhn1 : n % 2 = 1\nh : n = 0\n⊢ False",
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"zero_ne_one._simp_1",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.ModEq | {
"line": 568,
"column": 53
} | {
"line": 568,
"column": 61
} | [
{
"pp": "m n : ℕ\nhm1 : m % 2 = 1\nhn1 : n % 2 = 1\nh : n = 0\n⊢ False",
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"zero_ne_one._simp_1",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.ModEq | {
"line": 579,
"column": 2
} | {
"line": 579,
"column": 48
} | [
{
"pp": "n : ℕ\n⊢ n % 4 = 3 → n % 2 = 1",
"usedConstants": [
"HMul.hMul",
"congrArg",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instMulNat",
"instOfNatNat",
"Nat.ModEq.of_mul_left",
"HMod.hMod",
"Nat.ModEq",
"implies_congr",
"Nat",
"Eq... | simpa [ModEq] using @ModEq.of_mul_left 2 n 3 2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.Nat.ModEq | {
"line": 579,
"column": 2
} | {
"line": 579,
"column": 48
} | [
{
"pp": "n : ℕ\n⊢ n % 4 = 3 → n % 2 = 1",
"usedConstants": [
"HMul.hMul",
"congrArg",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instMulNat",
"instOfNatNat",
"Nat.ModEq.of_mul_left",
"HMod.hMod",
"Nat.ModEq",
"implies_congr",
"Nat",
"Eq... | simpa [ModEq] using @ModEq.of_mul_left 2 n 3 2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.ModEq | {
"line": 579,
"column": 2
} | {
"line": 579,
"column": 48
} | [
{
"pp": "n : ℕ\n⊢ n % 4 = 3 → n % 2 = 1",
"usedConstants": [
"HMul.hMul",
"congrArg",
"Eq.mp",
"Nat.instMod",
"instHMod",
"instMulNat",
"instOfNatNat",
"Nat.ModEq.of_mul_left",
"HMod.hMod",
"Nat.ModEq",
"implies_congr",
"Nat",
"Eq... | simpa [ModEq] using @ModEq.of_mul_left 2 n 3 2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ZMod.Defs | {
"line": 94,
"column": 20
} | {
"line": 94,
"column": 37
} | [
{
"pp": "n : ℕ\na b c : Fin n\n⊢ c * (a + b) = a * c + b * c",
"usedConstants": [
"_private.Mathlib.Data.ZMod.Defs.0.Fin.left_distrib_aux",
"Fin.instCommSemigroup",
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"congrArg",
"id",
"CommMagma.toMul",
"AddCommSe... | left_distrib_aux, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Finite | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 29
} | [
{
"pp": "α : Type u_1\n⊢ Nat.card α = 1 ↔ ∃ x, ∀ (y : α), y = x",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Exists",
"id",
"Nat.card",
"instOfNatNat",
"Nat.card_eq_one_iff_unique",
"And",
"Iff",
"Nat",
"propext",
"Nonempty",
"Subs... | rw [card_eq_one_iff_unique] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 257,
"column": 23
} | {
"line": 257,
"column": 32
} | [
{
"pp": "ι : Type u'\nR : Type u_2\nM : Type u_4\nv : ι → M\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nH :\n ∀ (s : Finset ι) (f g : ι → R), (∀ i ∉ s, f i = g i) → ∑ i ∈ s, f i • v i = ∑ i ∈ s, g i • v i → ∀ (i : ι), f i = g i\ns : Finset ι\nf g : ι → R\neq : ∑ i ∈ s, f i • v i = ∑ i ∈... | ite_smul, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.SetTheory.Cardinal.Finite | {
"line": 330,
"column": 6
} | {
"line": 330,
"column": 22
} | [
{
"pp": "n : ℕ\nc : Cardinal.{u_3}\n⊢ ↑n = toENat c ↔ ↑n = c",
"usedConstants": [
"Eq.mpr",
"ENat.instNatCast",
"Cardinal",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"OrderRingHom.in... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Finite | {
"line": 330,
"column": 23
} | {
"line": 330,
"column": 39
} | [
{
"pp": "n : ℕ\nc : Cardinal.{u_3}\n⊢ ↑n ≤ toENat c ∧ toENat c ≤ ↑n ↔ ↑n = c",
"usedConstants": [
"Eq.mpr",
"ENat.instNatCast",
"Cardinal",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 339,
"column": 44
} | {
"line": 339,
"column": 60
} | [
{
"pp": "ι : Type u'\nR : Type u_2\ns : Set ι\nM : Type u_4\nM' : Type u_5\nv : ι → M\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nhf_inj : InjOn ⇑f ↑(span R (v '' s))\n⊢ InjOn ⇑f ↑(span R (Set.range fun i ↦ v ↑i))",
"us... | ← image_eq_range | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Dimension.Basic | {
"line": 218,
"column": 57
} | {
"line": 218,
"column": 65
} | [
{
"pp": "R : Type u\nR' : Type u'\nM : Type v\nM' : Type v'\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R'\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R' M'\ni : R → R'\nj : M ≃+ M'\nhi : Bijective i\nhc : ∀ (r : R) (m : M), j (r • m) = i r • j m\nx✝¹ : R\nx✝ : M'\n⊢ i ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.LinearAlgebra.Dimension.Basic | {
"line": 218,
"column": 57
} | {
"line": 218,
"column": 65
} | [
{
"pp": "R : Type u\nR' : Type u'\nM : Type v\nM' : Type v'\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R'\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R' M'\ni : R → R'\nj : M ≃+ M'\nhi : Bijective i\nhc : ∀ (r : R) (m : M), j (r • m) = i r • j m\nx✝¹ : R\nx✝ : M'\n⊢ i ... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Dimension.Basic | {
"line": 218,
"column": 57
} | {
"line": 218,
"column": 65
} | [
{
"pp": "R : Type u\nR' : Type u'\nM : Type v\nM' : Type v'\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R'\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R' M'\ni : R → R'\nj : M ≃+ M'\nhi : Bijective i\nhc : ∀ (r : R) (m : M), j (r • m) = i r • j m\nx✝¹ : R\nx✝ : M'\n⊢ i ... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Dimension.Basic | {
"line": 254,
"column": 6
} | {
"line": 254,
"column": 22
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na✝ : Nontrivial R\n⊢ Module.rank R R = 1",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"Cardinal.instOne",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 618,
"column": 6
} | {
"line": 618,
"column": 59
} | [
{
"pp": "case h.e'_2.h.e'_5.a\nι : Type u'\nR : Type u_2\nM : Type u_4\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : LinearOrder R\ninst✝² : CanonicallyOrderedAdd R\ninst✝¹ : AddRightReflectLE R\ninst✝ : IsCancelAdd M\nthis✝ : Sub R := CanonicallyOrderedAdd.toSub\nthis... | · simp [hi.2, ← add_smul, tsub_add_cancel_of_le hi.2] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 652,
"column": 8
} | {
"line": 652,
"column": 22
} | [
{
"pp": "case refine_2\nι : Type u'\nR : Type u_2\nM : Type u_4\nv : ι → M\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\ninst✝⁵ : LinearOrder R\ninst✝⁴ : CanonicallyOrderedAdd R\ninst✝³ : AddRightReflectLE R\ninst✝² : IsCancelAdd M\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nh : ∀ (t : Fi... | intro i hi hi' | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 679,
"column": 4
} | {
"line": 684,
"column": 61
} | [
{
"pp": "case refine_2\nι : Type u'\nR : Type u_2\nM : Type u_4\nv : ι → M\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : LinearOrder R\ninst✝³ : CanonicallyOrderedAdd R\ninst✝² : AddRightReflectLE R\ninst✝¹ : IsCancelAdd M\ninst✝ : DecidableEq ι\ns : Finset ι\nh : ∀ t ⊆ s, ∀ (f :... | · conv =>
enter [2, 1, 1]
rw [← s.subtype_map_of_mem (fun x hx => hx), Finset.subtype_eq_univ.2 (fun x hx => hx)]
change Finset.map (Embedding.subtype (· ∈ (s : Set ι))) _
rw [← Finset.map_sdiff]
simpa [Embedding.subtype, ← Finset.compl_eq_univ_sdiff] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.LinearAlgebra.LinearIndependent.Defs | {
"line": 749,
"column": 23
} | {
"line": 749,
"column": 32
} | [
{
"pp": "ι : Type u'\nR : Type u_2\nM : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nv : ι → M\nH : ∀ (s : Finset ι) (g : ι → R), (∀ i ∉ s, g i = 0) → ∑ i ∈ s, g i • v i = 0 → ∀ (i : ι), g i = 0\ns : Finset ι\ng : ι → R\nhg : ∑ i ∈ s, g i • v i = 0\ni : ι\nhi : i ∈ s\n⊢ ∑ x ∈ s, (if x... | ite_smul, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finite.Card | {
"line": 165,
"column": 38
} | {
"line": 165,
"column": 55
} | [
{
"pp": "case inl\nα : Type u_1\ns t : Set α\nh : s.Finite ∧ t.Finite\n⊢ Nat.card ↑(s ∪ t) ≤ Nat.card ↑s + Nat.card ↑t",
"usedConstants": [
"congrArg",
"Finite",
"Set.Finite",
"Eq.mp",
"Set.Elem",
"Set.finite_coe_iff",
"And",
"propext",
"Eq.symm"
]
... | ← finite_coe_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Set.Card | {
"line": 534,
"column": 55
} | {
"line": 534,
"column": 85
} | [
{
"pp": "case h\nα : Type u_1\nβ : Type u_2\ninst✝ : Nonempty β\ns : Set α\nt : Set β\nhs : s.Finite\nhle : s.encard ≤ t.encard\na : α\nhas : a ∈ s\nb : β\nhbt : b ∈ t\nhle' : (s \\ {a}).encard ≤ (t \\ {b}).encard\nf₀ : α → β\nhinj : InjOn f₀ (s \\ {a})\nhf₀s : ∀ x ∈ s, ¬x = a → f₀ x ∈ t ∧ ¬f₀ x = b\n⊢ insert a... | injOn_insert (fun h ↦ h.2 rfl) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Set.Card | {
"line": 619,
"column": 93
} | {
"line": 622,
"column": 53
} | [
{
"pp": "α : Type u_1\ns : Set α\nk : ℕ\n⊢ s.encard ≤ ↑k ↔ s.Finite ∧ s.ncard ≤ k",
"usedConstants": [
"Eq.mpr",
"Set.encard",
"Set.ncard_def",
"ENat.instNatCast",
"congrArg",
"Set.Finite",
"Exists",
"id",
"and_congr_right_iff",
"LE.le",
"ins... | by
rw [encard_le_coe_iff, and_congr_right_iff]
exact fun hfin ↦ ⟨fun ⟨n₀, hn₀, hle⟩ ↦ by rwa [ncard_def, hn₀, ENat.toNat_coe],
fun h ↦ ⟨s.ncard, by rw [hfin.cast_ncard_eq], h⟩⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Set.Card | {
"line": 713,
"column": 2
} | {
"line": 714,
"column": 91
} | [
{
"pp": "α : Type u_1\na : α\ns : Set α\n⊢ s.ncard ≤ (insert a s).ncard",
"usedConstants": [
"Eq.mpr",
"Nat.zero_le",
"Set.Infinite.ncard",
"Set.finite_or_infinite",
"congrArg",
"Set.Finite",
"id",
"Insert.insert",
"instOfNatNat",
"LE.le",
"i... | refine
s.finite_or_infinite.elim (fun h ↦ ?_) (fun h ↦ by (rw [h.ncard]; exact Nat.zero_le _)) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Set.Card | {
"line": 1155,
"column": 11
} | {
"line": 1155,
"column": 23
} | [
{
"pp": "α : Type u_1\ns : Set α\nhft : Fintype ↑s\nh : ∃ a, s.toFinset = {a}\na : α\nha : s.toFinset = {a}\n⊢ s = {a}",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Data.Set.Card.0.Set.ncard_eq_one._simp_1_1",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Iff",
... | Set.ext_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Group.Graph | {
"line": 106,
"column": 8
} | {
"line": 106,
"column": 23
} | [
{
"pp": "G : Type u_1\nH : Type u_2\nI : Type u_3\ninst✝² : Monoid G\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nf : G →* H × I\nhf₁ : Surjective (Prod.fst ∘ ⇑f)\nhf₂ : Surjective (Prod.snd ∘ ⇑f)\nhf : ∀ (g₁ g₂ : G), (f g₁).1 = (f g₂).1 ↔ (f g₁).2 = (f g₂).2\ne₁ : H →* I\nhe₁ : mrange f = e₁.mgraph\ne₂ : I →* H\nhe₂ ... | SetLike.ext_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Congruence.Basic | {
"line": 279,
"column": 2
} | {
"line": 279,
"column": 37
} | [
{
"pp": "R : Type u_3\ninst✝¹ : Add R\ninst✝ : Mul R\nS : Set (RingCon R)\n⊢ sSup S = ringConGen (sSup (DFunLike.coe '' S))",
"usedConstants": [
"Eq.mpr",
"RingCon.instFunLikeForallProp",
"congrArg",
"iSup",
"Prop.instCompleteLattice",
"RingCon.instCompleteLattice",
... | rw [sSup_eq_ringConGen, sSup_image] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Pi | {
"line": 232,
"column": 2
} | {
"line": 237,
"column": 20
} | [
{
"pp": "R : Type u\nι : Type x\ninst✝³ : Semiring R\nφ : ι → Type i\ninst✝² : (i : ι) → AddCommMonoid (φ i)\ninst✝¹ : (i : ι) → Module R (φ i)\ninst✝ : DecidableEq ι\nI J : Set ι\nh : Disjoint I J\nb : (i : ι) → φ i\nhI : ∀ i ∈ Iᶜ, b i = 0\nhJ : ∀ i ∈ Jᶜ, b i = 0\ni : ι\n⊢ b i = 0 i",
"usedConstants": [
... | classical
by_cases hiI : i ∈ I
· by_cases hiJ : i ∈ J
· exact (h.le_bot ⟨hiI, hiJ⟩).elim
· exact hJ i hiJ
· exact hI i hiI | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.LinearAlgebra.Pi | {
"line": 253,
"column": 49
} | {
"line": 253,
"column": 69
} | [
{
"pp": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝¹³ : Semiring R\ninst✝¹² : AddCommMonoid M₂\ninst✝¹¹ : Module R M₂\ninst✝¹⁰ : AddCommMonoid M₃\ninst✝⁹ : Module R M₃\nφ : ι → Type i\ninst✝⁸ : (i : ι) → Ad... | simpa [apply_single] | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.LinearAlgebra.Pi | {
"line": 253,
"column": 49
} | {
"line": 253,
"column": 69
} | [
{
"pp": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝¹³ : Semiring R\ninst✝¹² : AddCommMonoid M₂\ninst✝¹¹ : Module R M₂\ninst✝¹⁰ : AddCommMonoid M₃\ninst✝⁹ : Module R M₃\nφ : ι → Type i\ninst✝⁸ : (i : ι) → Ad... | simpa [apply_single] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Pi | {
"line": 253,
"column": 49
} | {
"line": 253,
"column": 69
} | [
{
"pp": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝¹³ : Semiring R\ninst✝¹² : AddCommMonoid M₂\ninst✝¹¹ : Module R M₂\ninst✝¹⁰ : AddCommMonoid M₃\ninst✝⁹ : Module R M₃\nφ : ι → Type i\ninst✝⁸ : (i : ι) → Ad... | simpa [apply_single] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.SuccPred | {
"line": 74,
"column": 51
} | {
"line": 74,
"column": 59
} | [
{
"pp": "case h\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ succ b\nx : α\n⊢ x = succ b ∨ x ≤ b → x = succ b → a ≤ x",
"usedConstants": [
"Order.succ",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Interval.Set.SuccPred | {
"line": 151,
"column": 53
} | {
"line": 151,
"column": 61
} | [
{
"pp": "case h\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\nx : α\n⊢ x ≤ b → x = b → a ≤ x",
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Interval.Set.SuccPred | {
"line": 155,
"column": 51
} | {
"line": 155,
"column": 59
} | [
{
"pp": "case h\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a ≤ b\nx : α\n⊢ x = pred a ∨ a ≤ x → x = pred a → x ≤ b",
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.to... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Interval.Set.SuccPred | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 59
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a ≤ b\n⊢ insert (pred a) (Icc a b) = Icc (pred a) b",
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"M... | ext x; simp [or_and_left, pred_le_iff_eq_or_le]; simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.SuccPred | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 59
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a ≤ b\n⊢ insert (pred a) (Icc a b) = Icc (pred a) b",
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"M... | ext x; simp [or_and_left, pred_le_iff_eq_or_le]; simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 109,
"column": 44
} | {
"line": 111,
"column": 30
} | [
{
"pp": "ι : Type u_1\ninst✝ : LinearOrder ι\ni : ι\n⊢ i ≤ succFn i",
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"lowerBounds",
"congrArg",
"PartialOrder.toPreorder",
"le_of_lt",
"Preorder.toLE",
"LinearLocallyFiniteOrder.succFn",
"Membership.mem",
"S... | by
rw [le_isGLB_iff (succFn_spec i), mem_lowerBounds]
exact fun x hx ↦ le_of_lt hx | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 238,
"column": 71
} | {
"line": 238,
"column": 97
} | [
{
"pp": "ι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 i : ι\nhi : i0 ≤ i\n⊢ 0 ≤ ↑(Nat.find ⋯)",
"usedConstants": [
"Order.succ",
"LinearOrder.toDecidableEq",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder... | exact Int.natCast_nonneg _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 271,
"column": 4
} | {
"line": 271,
"column": 30
} | [
{
"pp": "case pos\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 : ι\nn : ℕ\nhn : ¬IsMax (succ^[n] i0)\nm : ℕ := (toZ i0 (succ^[n] i0)).toNat\nh_eq : succ^[m] i0 = succ^[n] i0\nhmn : m = n\n⊢ 0 ≤ ↑(Nat.find ⋯)",
"usedConstants": [
"Or... | exact Int.natCast_nonneg _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 30
} | [
{
"pp": "case pos\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 : ι\nn : ℕ\nhn : ¬IsMin (pred^[n + 1] i0)\nthis : pred^[n.succ] i0 < i0\nm : ℕ := (-toZ i0 (pred^[n.succ] i0)).toNat\nh_eq : pred^[m] i0 = pred^[n.succ] i0\nhmn : m = n + 1\n⊢ 0 ≤... | exact Int.natCast_nonneg _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.BigOperators.Intervals | {
"line": 261,
"column": 62
} | {
"line": 261,
"column": 70
} | [
{
"pp": "M : Type u_3\ninst✝ : CommGroup M\nn : ℕ\na : Fin n\nf : Fin (n + 1) → M\n⊢ ∀ a_1 ∈ range n,\n a_1 ∈ range (↑a + 1) →\n (if h : a_1 < n then if ⟨a_1, h⟩ ∈ Iic a then f ⟨a_1, h⟩.succ / f ⟨a_1, h⟩.castSucc else 1 else 1) =\n (if hi : a_1 + 1 < n + 1 then f ⟨a_1 + 1, hi⟩ else 1) / if hi : a... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Intervals | {
"line": 271,
"column": 4
} | {
"line": 271,
"column": 12
} | [
{
"pp": "case h.e'_2.a\nM : Type u_3\ninst✝ : CommGroup M\nn : ℕ\na b : Fin n\nhab : a ≤ b\nf : Fin (n + 1) → M\nx✝ : ℕ\na✝ : x✝ ∈ Icc ↑a ↑b\n⊢ (if h : x✝ < n then f ⟨x✝, h⟩.succ / f ⟨x✝, h⟩.castSucc else 1) =\n (if hi : x✝ + 1 < n + 1 then f ⟨x✝ + 1, hi⟩ else 1) / if hi : x✝ < n + 1 then f ⟨x✝, hi⟩ else 1",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Ideal.Span | {
"line": 190,
"column": 32
} | {
"line": 190,
"column": 48
} | [
{
"pp": "α : Type u\ninst✝¹ : CommSemiring α\ninst✝ : IsDomain α\nx y : α\n⊢ span {x} = span {y} ↔ x ∣ y ∧ y ∣ x",
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"semigroupDvd",
"P... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Ideal.Maximal | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 12
} | [
{
"pp": "α : Type u\ninst✝ : CommSemiring α\nS : Submonoid α\ndisjoint : Disjoint ↑⊤ ↑S\nmaximally_disjoint : ∀ (J : Ideal α), ⊤ < J → ¬Disjoint ↑J ↑S\nthis : 1 ∈ ↑S\n⊢ False",
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Semiring.toModule",
"ChainCompleteP... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Module.Submodule.IterateMapComap | {
"line": 77,
"column": 14
} | {
"line": 77,
"column": 23
} | [
{
"pp": "case zero.zero\nR : Type u_1\nN : Type u_2\nM : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf i : N →ₗ[R] M\nK : Submodule R N\nhf : Surjective ⇑f\nhi : Injective ⇑i\nheq : f.iterateMapComap i 0 K ≠ f.iterateMapComap i (0 +... | exact heq | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Module.Submodule.IterateMapComap | {
"line": 77,
"column": 14
} | {
"line": 77,
"column": 23
} | [
{
"pp": "case zero.zero\nR : Type u_1\nN : Type u_2\nM : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf i : N →ₗ[R] M\nK : Submodule R N\nhf : Surjective ⇑f\nhi : Injective ⇑i\nheq : f.iterateMapComap i 0 K ≠ f.iterateMapComap i (0 +... | exact heq | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Submodule.IterateMapComap | {
"line": 77,
"column": 14
} | {
"line": 77,
"column": 23
} | [
{
"pp": "case zero.zero\nR : Type u_1\nN : Type u_2\nM : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf i : N →ₗ[R] M\nK : Submodule R N\nhf : Surjective ⇑f\nhi : Injective ⇑i\nheq : f.iterateMapComap i 0 K ≠ f.iterateMapComap i (0 +... | exact heq | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Ideal.Basic | {
"line": 100,
"column": 58
} | {
"line": 100,
"column": 81
} | [
{
"pp": "α : Type u_6\ninst✝ : Semiring α\nI : Ideal α\na b : α\nm n : ℕ\nha : a ^ m ∈ I\nhb : b ^ n ∈ I\nhab : Commute a b\n⊢ m + n ≤ m + n - 1 + 1",
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Nat.sub_le_iff_le_add",
"id",
"instSubNat",
"instOfNatNat",
... | ← Nat.sub_le_iff_le_add | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Ideal.Basic | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 31
} | [
{
"pp": "case cons\nα : Type u_2\ninst✝¹ : CommSemiring α\ninst✝ : DecidableEq α\nn : ℕ\na : α\ns : Multiset α\nhs : s.sum ^ (s.card * n + 1) ∈ span ↑(Multiset.map (fun x ↦ x ^ (n + 1)) s).toFinset\n⊢ ∑ m ∈ Finset.range ((s.card + 1) * n + 1 + 1),\n a ^ m * s.sum ^ ((s.card + 1) * n + 1 - m) * ↑(((s.card +... | refine Submodule.sum_mem _ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 131,
"column": 73
} | {
"line": 131,
"column": 81
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nP : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : P × M →ₗ[R] M\nx : ℕ →₀ P\n⊢ ∀ x_1 ∈ x.support, (x_1 ∉ Set.range fun x ↦ x + 1) → ((((inr R P M ∘ₗ f) ^ x_1) ∘ₗ inl R P M) (x x_1)).2 = 0",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 131,
"column": 73
} | {
"line": 131,
"column": 81
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nP : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : P × M →ₗ[R] M\nx : ℕ →₀ P\n⊢ ∀ x_1 ∈ x.support, (x_1 ∉ Set.range fun x ↦ x + 1) → ((((inr R P M ∘ₗ f) ^ x_1) ∘ₗ inl R P M) (x x_1)).2 = 0",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 131,
"column": 73
} | {
"line": 131,
"column": 81
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nP : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : P × M →ₗ[R] M\nx : ℕ →₀ P\n⊢ ∀ x_1 ∈ x.support, (x_1 ∉ Set.range fun x ↦ x + 1) → ((((inr R P M ∘ₗ f) ^ x_1) ∘ₗ inl R P M) (x x_1)).2 = 0",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 142,
"column": 17
} | {
"line": 142,
"column": 27
} | [
{
"pp": "case inr\nR : Type u_1\nM : Type u_2\nP : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : P × M →ₗ[R] M\ninj : Injective ⇑f\nx y : ℕ →₀ P\ns : Finset ℕ := x.support ∪ y.support\nne : s.Nonempty\nn : ℕ\nhn : n = s.max' ne\n⊢... | revert x y | Lean.Elab.Tactic.evalRevert | Lean.Parser.Tactic.revert |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 226,
"column": 49
} | {
"line": 226,
"column": 57
} | [
{
"pp": "case h\nR : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nf : M →ₗ[R] N\nhf : f.ker = ⊥\nI : Type u_6\nx : I →₀ N\ny : I → M\nhy : ∀ (i : I), f (y i) = x i\na✝ : I\n⊢ ((mapRange.linearMap f) { supp... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Filter.Map | {
"line": 316,
"column": 48
} | {
"line": 317,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ng : β → α\nhfg : LeftInverse g f\nF : Filter α\n⊢ comap f (comap g F) = F",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Filter.comap_comap",
"Filter.comap_id",
"Function.LeftInverse.comp_eq_id",
... | by
rw [comap_comap, hfg.comp_eq_id, comap_id] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Filter.Map | {
"line": 383,
"column": 33
} | {
"line": 383,
"column": 50
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : α → β\ns : Set α\ng : Filter β\n⊢ comap m g ≤ 𝓟 s ↔ g ≤ 𝓟 (kernImage m s)",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.le_principal_iff",
"Set.kernImage",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.... | le_principal_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Filter.Map | {
"line": 383,
"column": 51
} | {
"line": 383,
"column": 68
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : α → β\ns : Set α\ng : Filter β\n⊢ s ∈ comap m g ↔ g ≤ 𝓟 (kernImage m s)",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.le_principal_iff",
"Set.kernImage",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toL... | le_principal_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Filter.Map | {
"line": 493,
"column": 22
} | {
"line": 493,
"column": 58
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nhf : Surjective f\nl : Filter β\n⊢ range f ∈ l",
"usedConstants": [
"Filter.instMembership",
"congrArg",
"Set.univ",
"Membership.mem",
"Function.Surjective.range_eq",
"_private.Mathlib.Order.Filter.Map.0.Filter.map_comap_of_... | by simp only [hf.range_eq, univ_mem] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Filter.AtTopBot.Disjoint | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 22
} | [
{
"pp": "α : Type u_3\ninst✝¹ : PartialOrder α\ninst✝ : Nontrivial α\nx y : α\nhne : x ≠ y\n⊢ Disjoint atBot atTop",
"usedConstants": [
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"Disjoint",
"CompleteLattice.... | by_cases hle : x ≤ y | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Order.Filter.Map | {
"line": 877,
"column": 4
} | {
"line": 877,
"column": 28
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ng : α → β\nf : Filter α\ns : Set α\nhs : s ∈ f\n⊢ {g} ∈ pure g",
"usedConstants": [
"Filter.singleton_mem_pure"
]
}
] | exact singleton_mem_pure | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Filter.Basic | {
"line": 1228,
"column": 2
} | {
"line": 1228,
"column": 65
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup β\nl : Filter α\nf₁ f₂ g₁ g₂ : α → β\nhf : f₁ ≤ᶠ[l] f₂\nhg : g₁ ≤ᶠ[l] g₂\n⊢ f₁ ⊔ g₁ ≤ᶠ[l] f₂ ⊔ g₂",
"usedConstants": [
"sup_le_sup",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Filter.mp_m... | filter_upwards [hf, hg] with x hfx hgx using sup_le_sup hfx hgx | Mathlib.Tactic._aux_Mathlib_Order_Filter_Defs___elabRules_Mathlib_Tactic_filterUpwards_1 | Mathlib.Tactic.filterUpwards |
Mathlib.Order.Filter.Basic | {
"line": 1228,
"column": 2
} | {
"line": 1228,
"column": 65
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup β\nl : Filter α\nf₁ f₂ g₁ g₂ : α → β\nhf : f₁ ≤ᶠ[l] f₂\nhg : g₁ ≤ᶠ[l] g₂\n⊢ f₁ ⊔ g₁ ≤ᶠ[l] f₂ ⊔ g₂",
"usedConstants": [
"sup_le_sup",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Filter.mp_m... | filter_upwards [hf, hg] with x hfx hgx using sup_le_sup hfx hgx | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.Basic | {
"line": 1228,
"column": 2
} | {
"line": 1228,
"column": 65
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup β\nl : Filter α\nf₁ f₂ g₁ g₂ : α → β\nhf : f₁ ≤ᶠ[l] f₂\nhg : g₁ ≤ᶠ[l] g₂\n⊢ f₁ ⊔ g₁ ≤ᶠ[l] f₂ ⊔ g₂",
"usedConstants": [
"sup_le_sup",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Filter.mp_m... | filter_upwards [hf, hg] with x hfx hgx using sup_le_sup hfx hgx | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.AtTopBot.Basic | {
"line": 209,
"column": 47
} | {
"line": 209,
"column": 64
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝² : Nonempty α\ninst✝¹ : Preorder α\ninst✝ : IsDirectedOrder α\nf : α → β\ns : Set β\n⊢ atTop ≤ 𝓟 (f ⁻¹' s) ↔ ∃ N, ∀ n ≥ N, f n ∈ s",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorde... | le_principal_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.Finiteness.Defs | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 18
} | [
{
"pp": "case mp.a\nR : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set M\ns'' : Finset M\nhs'' : span R ↑s'' = span R s\ns' : Finset M\nhs's : ↑s' ⊆ s\nhss' : ↑s'' ⊆ ↑(span R ↑s')\n⊢ span R ↑s' ≤ span R s",
"usedConstants": [
"Eq.mpr",
"Submodu... | rw [span_le] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Finiteness.Basic | {
"line": 78,
"column": 26
} | {
"line": 85,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\nι : Type u_5\nM : ι → Type u_6\ninst✝² : Finite ι\ninst✝¹ : (i : ι) → AddCommMonoid (M i)\ninst✝ : (i : ι) → Module R (M i)\np : (i : ι) → Submodule R (M i)\nhsb : ∀ (i : ι), (p i).FG\n⊢ (pi univ p).FG",
"usedConstants": [
"Eq.mpr",
"Submodule",
... | by
classical
simp_rw [fg_def] at hsb ⊢
choose t htf hts using hsb
refine
⟨⋃ i, (LinearMap.single R _ i) '' t i, Set.finite_iUnion fun i => (htf i).image _, ?_⟩
-- Note: https://github.com/leanprover-community/mathlib4/pull/8386 changed `span_image` into `span_image _`
simp_rw [span_iUnion, s... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.IsNormal | {
"line": 66,
"column": 36
} | {
"line": 67,
"column": 83
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\na : α\nf : α → β\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nhf : IsNormal f\nha : IsSuccLimit a\nb : β\n⊢ b < f a ↔ ∃ a' < a, b < f a'",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Order.IsNormal.isLUB_image_Iio_of_isSuccLimit",
"exists_... | by
simpa [mem_upperBounds] using lt_isLUB_iff (hf.isLUB_image_Iio_of_isSuccLimit ha) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.IsNormal | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 12
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\nf : α → β\ninst✝⁴ : LinearOrder α\ninst✝³ : WellFoundedLT α\ninst✝² : SuccOrder α\ninst✝¹ : LinearOrder β\ninst✝ : OrderBot α\ng : α → β\nhf : IsNormal f\nhg : IsNormal g\n⊢ f = g → f ⊥ = g ⊥ ∧ ∀ (a : α), f a = g a → f (succ a) = g (succ a)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.IsNormal | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 12
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\nf : α → β\ninst✝⁴ : LinearOrder α\ninst✝³ : WellFoundedLT α\ninst✝² : SuccOrder α\ninst✝¹ : LinearOrder β\ninst✝ : OrderBot α\ng : α → β\nhf : IsNormal f\nhg : IsNormal g\n⊢ f = g → f ⊥ = g ⊥ ∧ ∀ (a : α), f a = g a → f (succ a) = g (succ a)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.IsNormal | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 12
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\nf : α → β\ninst✝⁴ : LinearOrder α\ninst✝³ : WellFoundedLT α\ninst✝² : SuccOrder α\ninst✝¹ : LinearOrder β\ninst✝ : OrderBot α\ng : α → β\nhf : IsNormal f\nhg : IsNormal g\n⊢ f = g → f ⊥ = g ⊥ ∧ ∀ (a : α), f a = g a → f (succ a) = g (succ a)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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