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.Order.WithBot | {
"line": 454,
"column": 14
} | {
"line": 454,
"column": 22
} | [
{
"pp": "case coe\nα : Type u_1\na : α\ninst✝ : LE α\nx a✝ : α\nh : ↑x ≤ ↑a✝\n⊢ unbotD a ↑x ≤ unbotD a ↑a✝",
"usedConstants": [
"WithBot.some",
"WithBot",
"WithBot.coe_le_coe._simp_2",
"Eq.mp",
"id",
"LE.le",
"WithBot.instLE"
]
}
] | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.WithBot | {
"line": 454,
"column": 2
} | {
"line": 454,
"column": 22
} | [
{
"pp": "α : Type u_1\na : α\ninst✝ : LE α\ny : WithBot α\nx : α\nh : ↑x ≤ y\n⊢ unbotD a ↑x ≤ unbotD a y",
"usedConstants": [
"False",
"WithBot.some",
"WithBot",
"WithBot.coe_le_coe._simp_2",
"False.elim",
"WithBot.coe_ne_bot._simp_3",
"Eq.mp",
"id",
"Bo... | cases y <;> simp_all | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Order.WithBot | {
"line": 644,
"column": 13
} | {
"line": 644,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : Nonempty α\ninst✝ : NoTopOrder α\nx : WithBot (WithTop α)\n⊢ x = ⊤ → ∀ (a : α), ↑↑a ≤ x",
"usedConstants": [
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.WithBot | {
"line": 644,
"column": 13
} | {
"line": 644,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : Nonempty α\ninst✝ : NoTopOrder α\nx : WithBot (WithTop α)\n⊢ x = ⊤ → ∀ (a : α), ↑↑a ≤ x",
"usedConstants": [
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.WithBot | {
"line": 644,
"column": 13
} | {
"line": 644,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : Nonempty α\ninst✝ : NoTopOrder α\nx : WithBot (WithTop α)\n⊢ x = ⊤ → ∀ (a : α), ↑↑a ≤ x",
"usedConstants": [
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 154,
"column": 2
} | {
"line": 155,
"column": 72
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\nH : DenselyOrdered α\n⊢ Nontrivial αˣ",
"usedConstants": [
"Nontrivial",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"MulOne.toOne... | · obtain ⟨x, hx, hx'⟩ := exists_between (zero_lt_one' α)
exact ⟨Units.mk0 x hx.ne', 1, by simpa [Units.ext_iff] using hx'.ne⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 169,
"column": 47
} | {
"line": 171,
"column": 7
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\na b c d : α\nm n : ℕ\ninst✝ : DenselyOrdered α\n⊢ Nontrivial αˣ",
"usedConstants": [
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Pr... | by
have := denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units (α := α)
tauto | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 175,
"column": 51
} | {
"line": 177,
"column": 7
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\na b c d : α\nm n : ℕ\ninst✝ : DenselyOrdered α\n⊢ DenselyOrdered αˣ",
"usedConstants": [
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
... | by
have := denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units (α := α)
tauto | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 179,
"column": 89
} | {
"line": 181,
"column": 7
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : Nontrivial αˣ\n⊢ DenselyOrdered αˣ ↔ DenselyOrdered α",
"usedConstants": [
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Preorder.toLT",
... | by
have := denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units (α := α)
tauto | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 540,
"column": 64
} | {
"line": 541,
"column": 66
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : WithZero (Multiplicative G)\nhx : x ≠ 0\n⊢ x.log ≤ a ↔ x ≤ exp a",
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Iff.rfl",
"Preorder.toLE",
"WithZero.log",
"Exists",
... | by
lift x to Multiplicative G using hx; simpa [log, exp] using .rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 543,
"column": 64
} | {
"line": 544,
"column": 66
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : WithZero (Multiplicative G)\nhx : x ≠ 0\n⊢ x.log < a ↔ x < exp a",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"WithZero.coe_lt_coe._simp_1",
"Iff.rfl",
"... | by
lift x to Multiplicative G using hx; simpa [log, exp] using .rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 546,
"column": 64
} | {
"line": 547,
"column": 66
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : WithZero (Multiplicative G)\nhx : x ≠ 0\n⊢ a ≤ x.log ↔ exp a ≤ x",
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Iff.rfl",
"Preorder.toLE",
"WithZero.log",
"Exists",
... | by
lift x to Multiplicative G using hx; simpa [log, exp] using .rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 549,
"column": 64
} | {
"line": 550,
"column": 66
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : WithZero (Multiplicative G)\nhx : x ≠ 0\n⊢ a < x.log ↔ exp a < x",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"WithZero.coe_lt_coe._simp_1",
"Iff.rfl",
"... | by
lift x to Multiplicative G using hx; simpa [log, exp] using .rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.WithBot | {
"line": 980,
"column": 78
} | {
"line": 980,
"column": 86
} | [
{
"pp": "case bot.bot\nα : Type u_1\ninst✝ : LE α\n⊢ WithBot.ofDual ⊥ ≤ WithBot.ofDual ⊥ ↔ ⊥ ≤ ⊥",
"usedConstants": [
"OrderDual.instLE",
"WithBot",
"Equiv.instEquivLike",
"congrArg",
"WithBot.instOrderBot",
"le_top._simp_2",
"Equiv",
"Bot.bot",
"LE.le",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.WithBot | {
"line": 980,
"column": 78
} | {
"line": 980,
"column": 86
} | [
{
"pp": "case bot.coe\nα : Type u_1\ninst✝ : LE α\na✝ : αᵒᵈ\n⊢ WithBot.ofDual ⊥ ≤ WithBot.ofDual ↑a✝ ↔ ↑a✝ ≤ ⊥",
"usedConstants": [
"OrderDual.instLE",
"False",
"WithBot.some",
"WithBot",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"congrArg",
"WithTop.coe_ne_t... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.WithBot | {
"line": 980,
"column": 78
} | {
"line": 980,
"column": 86
} | [
{
"pp": "case coe.bot\nα : Type u_1\ninst✝ : LE α\na✝ : αᵒᵈ\n⊢ WithBot.ofDual ↑a✝ ≤ WithBot.ofDual ⊥ ↔ ⊥ ≤ ↑a✝",
"usedConstants": [
"OrderDual.instLE",
"WithBot.some",
"WithBot",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"congrArg",
"WithBot.instOrderBot",
"l... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.WithBot | {
"line": 980,
"column": 78
} | {
"line": 980,
"column": 86
} | [
{
"pp": "case coe.coe\nα : Type u_1\ninst✝ : LE α\na✝¹ a✝ : αᵒᵈ\n⊢ WithBot.ofDual ↑a✝¹ ≤ WithBot.ofDual ↑a✝ ↔ ↑a✝ ≤ ↑a✝¹",
"usedConstants": [
"OrderDual.instLE",
"WithBot.some",
"WithBot",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"WithBot.coe_le_coe._simp_2",
"Wit... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\nn : ℕ\nha : 0 ≤ a\n⊢ ⌊a⌋₊ = n ↔ n ≤ ⌊a⌋₊ ∧ ⌊a⌋₊ ≤ n",
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 134,
"column": 24
} | {
"line": 134,
"column": 40
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorSemiring R\na : R\nn : ℕ\ninst✝ : IsStrictOrderedRing R\nhn : n ≠ 0\n⊢ ⌊a⌋₊ = n ↔ n ≤ ⌊a⌋₊ ∧ ⌊a⌋₊ ≤ n",
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semila... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\nn : ℕ\nhn : n ≠ 0\n⊢ ⌈a⌉₊ = n ↔ n ≤ ⌈a⌉₊ ∧ ⌈a⌉₊ ≤ n",
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Divisibility.Basic | {
"line": 35,
"column": 2
} | {
"line": 36,
"column": 20
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Semigroup α\ninst✝² : Semigroup β\nF : Type u_3\ninst✝¹ : EquivLike F α β\ninst✝ : MulEquivClass F α β\nf : F\na : α\nb : β\n⊢ f a ∣ b ↔ a ∣ (↑f).symm b",
"usedConstants": [
"Semigroup.toMul",
"MulEquiv.instEquivLike",
"Dvd.dvd",
"congrAr... | obtain ⟨c, rfl⟩ : ∃ c, f c = b := EquivLike.surjective f b
simp [map_dvd_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Divisibility.Basic | {
"line": 35,
"column": 2
} | {
"line": 36,
"column": 20
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Semigroup α\ninst✝² : Semigroup β\nF : Type u_3\ninst✝¹ : EquivLike F α β\ninst✝ : MulEquivClass F α β\nf : F\na : α\nb : β\n⊢ f a ∣ b ↔ a ∣ (↑f).symm b",
"usedConstants": [
"Semigroup.toMul",
"MulEquiv.instEquivLike",
"Dvd.dvd",
"congrAr... | obtain ⟨c, rfl⟩ : ∃ c, f c = b := EquivLike.surjective f b
simp [map_dvd_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.NAry | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 41
} | [
{
"pp": "α : Type u_1\nβ : Type u_3\nγ : Type u_5\nf : α → β → γ\ns s' : Set α\nt t' : Set β\nhs : s ⊆ s'\nht : t ⊆ t'\na : α\nha : a ∈ s\nb : β\nhb : b ∈ t\n⊢ f a b ∈ image2 f s' t'",
"usedConstants": [
"Set.mem_image2_of_mem"
]
}
] | exact mem_image2_of_mem (hs ha) (ht hb) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 164,
"column": 34
} | {
"line": 164,
"column": 42
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝² : CommRing α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedRing α\na : ℤˣ\nh✝ : a = 1\n⊢ |↑↑a| = 1",
"usedConstants": [
"Int.cast",
"Units.val",
"MulOne.toOne",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"abs",
"congrAr... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 164,
"column": 34
} | {
"line": 164,
"column": 42
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝² : CommRing α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedRing α\na : ℤˣ\nh✝ : a = -1\n⊢ |↑↑a| = 1",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Units.val",
"NegZeroClass.toNeg",
"abs_neg",
"Mu... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 184,
"column": 57
} | {
"line": 184,
"column": 75
} | [
{
"pp": "case succ\nα : Type u_1\ninst✝ : CommRing α\na b : α\nn✝ n : ℕ\nih : a ^ (n + 1) - b ^ (n + 1) = (a - b) * geomSum a b n\n⊢ a ^ (n + 1 + 1) - b ^ (n + 1 + 1) = a ^ (n + 1 + 1) - a * b ^ (n + 1) + (a * b ^ (n + 1) - b ^ (n + 1 + 1))",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNo... | sub_add_sub_cancel | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Bounds.Image | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 57
} | [
{
"pp": "case refine_2\nα : Type u\nπ : α → Type u_1\ninst✝ : (a : α) → Preorder (π a)\ns : Set ((a : α) → π a)\nf : (a : α) → π a\nH : ∀ (a : α), IsLUB (eval a '' s) (f a)\n⊢ f ∈ upperBounds s",
"usedConstants": [
"lowerBounds",
"Preorder.toLE",
"Membership.mem",
"upperBounds",
... | exact fun g hg a => (H a).1 (mem_image_of_mem _ hg) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Bounds.Image | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 57
} | [
{
"pp": "case refine_2\nα : Type u\nπ : α → Type u_1\ninst✝ : (a : α) → Preorder (π a)\ns : Set ((a : α) → π a)\nf : (a : α) → π a\nH : ∀ (a : α), IsLUB (eval a '' s) (f a)\n⊢ f ∈ upperBounds s",
"usedConstants": [
"lowerBounds",
"Preorder.toLE",
"Membership.mem",
"upperBounds",
... | exact fun g hg a => (H a).1 (mem_image_of_mem _ hg) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Bounds.Image | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 57
} | [
{
"pp": "case refine_2\nα : Type u\nπ : α → Type u_1\ninst✝ : (a : α) → Preorder (π a)\ns : Set ((a : α) → π a)\nf : (a : α) → π a\nH : ∀ (a : α), IsLUB (eval a '' s) (f a)\n⊢ f ∈ upperBounds s",
"usedConstants": [
"lowerBounds",
"Preorder.toLE",
"Membership.mem",
"upperBounds",
... | exact fun g hg a => (H a).1 (mem_image_of_mem _ hg) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 499,
"column": 2
} | {
"line": 499,
"column": 45
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\na b : α\n⊢ (Icc a b).Subsingleton ↔ b ≤ a",
"usedConstants": [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"Set.Icc",
"Iff.intro",
"Set.Subsingl... | refine ⟨fun h ↦ ?_, subsingleton_Icc_of_ge⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Tactic.NormNum.Basic | {
"line": 211,
"column": 10
} | {
"line": 211,
"column": 13
} | [
{
"pp": "case eq\nα : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁✝ : na * db + nb * da = k * nc\nh₂✝ : da * db = k * dc\nthis✝ : Invertible ↑(da * db)\nthis : Invertible ↑dc\nH : ∀ (a : α), a * ⅟↑da * ⅟↑db = a * ⅟↑db * ⅟↑da\nh₁ : ↑na * ⅟↑da + ↑nb * ⅟↑... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 233,
"column": 10
} | {
"line": 233,
"column": 13
} | [
{
"pp": "case eq\nα : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁✝ : na * ↑db + nb * ↑da = ↑k * nc\nh₂✝ : da * db = k * dc\nthis✝ : Invertible ↑(da * db)\nthis : Invertible ↑dc\nH : ∀ (a : α), a * ⅟↑da * ⅟↑db = a * ⅟↑db * ⅟↑da\nh₁ : ↑na * ⅟↑da + ↑nb ... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 459,
"column": 49
} | {
"line": 459,
"column": 52
} | [
{
"pp": "α : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁✝ : na * nb = k * nc\nh₂✝ : da * db = k * dc\nthis✝ : Invertible ↑(da * db)\nthis : Invertible ↑dc\nH : ∀ (a : α), a * ⅟↑da * ⅟↑db = a * ⅟↑db * ⅟↑da\nh₁ : ↑na * ↑nb = ↑k * ↑nc\nh₂ : ↑nc * ⅟↑dc = ... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 479,
"column": 49
} | {
"line": 479,
"column": 52
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁✝ : na * nb = ↑k * nc\nh₂✝ : da * db = k * dc\nthis✝ : Invertible ↑(da * db)\nthis : Invertible ↑dc\nH : ∀ (a : α), a * ⅟↑da * ⅟↑db = a * ⅟↑db * ⅟↑da\nh₁ : ↑na * ↑nb = ↑k * ↑nc\nh₂ : ↑nc * ⅟↑dc ... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.Abel | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝ : AddCommMonoid α\nn₁ : ℕ\nx a₁ : α\nn₂ : ℕ\na₂ : α\nn' : ℕ\na' : α\nh₁ : n₁ + n₂ = n'\nh₂ : a₁ + a₂ = a'\n⊢ term n₁ x a₁ + term n₂ x a₂ = term n' x a'",
"usedConstants": [
"instHSMul",
"AddMonoid.toAddSemigroup",
"add_left_comm",
"congrArg",
"add_a... | simp [h₁.symm, h₂.symm, term, add_nsmul, add_assoc, add_left_comm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.Abel | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝ : AddCommMonoid α\nn₁ : ℕ\nx a₁ : α\nn₂ : ℕ\na₂ : α\nn' : ℕ\na' : α\nh₁ : n₁ + n₂ = n'\nh₂ : a₁ + a₂ = a'\n⊢ term n₁ x a₁ + term n₂ x a₂ = term n' x a'",
"usedConstants": [
"instHSMul",
"AddMonoid.toAddSemigroup",
"add_left_comm",
"congrArg",
"add_a... | simp [h₁.symm, h₂.symm, term, add_nsmul, add_assoc, add_left_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.Abel | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝ : AddCommMonoid α\nn₁ : ℕ\nx a₁ : α\nn₂ : ℕ\na₂ : α\nn' : ℕ\na' : α\nh₁ : n₁ + n₂ = n'\nh₂ : a₁ + a₂ = a'\n⊢ term n₁ x a₁ + term n₂ x a₂ = term n' x a'",
"usedConstants": [
"instHSMul",
"AddMonoid.toAddSemigroup",
"add_left_comm",
"congrArg",
"add_a... | simp [h₁.symm, h₂.symm, term, add_nsmul, add_assoc, add_left_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Field.Basic | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 52
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\ns : Set α\nha✝ : 0 ≤ a\nhs : IsGLB s b\nha : 0 < a\n⊢ IsGLB ((fun b ↦ a * b) '' s) (a * b)",
"usedConstants": [
"Iff.mpr",
"OrderIso.isGLB_image'",
... | · exact (OrderIso.mulLeft₀ _ ha).isGLB_image'.2 hs | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Order.Field.Basic | {
"line": 354,
"column": 6
} | {
"line": 354,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b c : α\nhc : c < 0\n⊢ a ≤ b / c ↔ b ≤ a * c",
"usedConstants": [
"Eq.mpr",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"... | ← neg_neg c, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b c : α\nhc : c < 0\n⊢ a < b / c ↔ b < a * c",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
... | ← neg_neg c, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.TakeDrop | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 14
} | [
{
"pp": "case pos\nα : Type u\na : α\nl : List α\nih : ∀ (h : l ≠ []), drop (l.length - 1) l = [l.getLast h]\nh : a :: l ≠ []\nhl : l = []\n⊢ drop ((a :: l).length - 1) (a :: l) = [(a :: l).getLast h]",
"usedConstants": [
"List.getLast",
"congrArg",
"HSub.hSub",
"instSubNat",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.TakeDrop | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 14
} | [
{
"pp": "case pos\nα : Type u\na : α\nl : List α\nih : ∀ (h : l ≠ []), drop (l.length - 1) l = [l.getLast h]\nh : a :: l ≠ []\nhl : l = []\n⊢ drop ((a :: l).length - 1) (a :: l) = [(a :: l).getLast h]",
"usedConstants": [
"List.getLast",
"congrArg",
"HSub.hSub",
"instSubNat",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.TakeDrop | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 14
} | [
{
"pp": "case pos\nα : Type u\na : α\nl : List α\nih : ∀ (h : l ≠ []), drop (l.length - 1) l = [l.getLast h]\nh : a :: l ≠ []\nhl : l = []\n⊢ drop ((a :: l).length - 1) (a :: l) = [(a :: l).getLast h]",
"usedConstants": [
"List.getLast",
"congrArg",
"HSub.hSub",
"instSubNat",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.InsertIdx | {
"line": 51,
"column": 45
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case zero.nil\nα : Type u\na : α\nhn : 0 ≠ [].length\n⊢ ([].eraseIdx 0).insertIdx 0 a = [].set 0 a",
"usedConstants": [
"False",
"List.eraseIdx",
"congrArg",
"False.elim",
"List.insertIdx",
"Eq.mp",
"not_true_eq_false",
"List.set",
"Ne",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.InsertIdx | {
"line": 51,
"column": 45
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case zero.cons\nα : Type u\na head✝ : α\ntail✝ : List α\nhn : 0 ≠ (head✝ :: tail✝).length\n⊢ ((head✝ :: tail✝).eraseIdx 0).insertIdx 0 a = (head✝ :: tail✝).set 0 a",
"usedConstants": [
"List.eraseIdx",
"congrArg",
"List.insertIdx",
"List.eraseIdx_zero",
"instOfNatNat",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.InsertIdx | {
"line": 51,
"column": 45
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case succ.nil\nα : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {l : List α}, n✝ ≠ l.length → (l.eraseIdx n✝).insertIdx n✝ a = l.set n✝ a\nhn : n✝ + 1 ≠ [].length\n⊢ ([].eraseIdx (n✝ + 1)).insertIdx (n✝ + 1) a = [].set (n✝ + 1) a",
"usedConstants": [
"List",
"eq_self",
"of_eq_true",
"Eq",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.InsertIdx | {
"line": 51,
"column": 45
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case succ.cons\nα : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {l : List α}, n✝ ≠ l.length → (l.eraseIdx n✝).insertIdx n✝ a = l.set n✝ a\nhead✝ : α\ntail✝ : List α\nhn : n✝ + 1 ≠ (head✝ :: tail✝).length\n⊢ ((head✝ :: tail✝).eraseIdx (n✝ + 1)).insertIdx (n✝ + 1) a = (head✝ :: tail✝).set (n✝ + 1) a",
"usedConstan... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.InsertIdx | {
"line": 76,
"column": 30
} | {
"line": 76,
"column": 38
} | [
{
"pp": "case succ.nil\nα : Type u\nβ : Type v\np : α → Prop\nf : (a : α) → p a → β\na : α\nha : p a\nn : ℕ\nihn : ∀ {l : List α} (hl : ∀ (x : α), x ∈ l → p x), (pmap f l hl).insertIdx n (f a ha) = pmap f (l.insertIdx n a) ⋯\nhl : ∀ (x : α), x ∈ [] → p x\n⊢ (pmap f [] hl).insertIdx (n + 1) (f a ha) = pmap f ([]... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.InsertIdx | {
"line": 76,
"column": 30
} | {
"line": 76,
"column": 38
} | [
{
"pp": "case succ.cons\nα : Type u\nβ : Type v\np : α → Prop\nf : (a : α) → p a → β\na : α\nha : p a\nn : ℕ\nihn : ∀ {l : List α} (hl : ∀ (x : α), x ∈ l → p x), (pmap f l hl).insertIdx n (f a ha) = pmap f (l.insertIdx n a) ⋯\nhead✝ : α\ntail✝ : List α\nhl : ∀ (x : α), x ∈ head✝ :: tail✝ → p x\n⊢ (pmap f (head✝... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Field.Basic | {
"line": 545,
"column": 36
} | {
"line": 545,
"column": 63
} | [
{
"pp": "case h.e'_4\nα : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na : α\na2 : 2 ≤ a\n⊢ 1 = 2 * 2⁻¹",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulO... | mul_inv_cancel₀ two_ne_zero | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 588,
"column": 4
} | {
"line": 588,
"column": 43
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\n⊢ 1 < a / b ↔ 0 < b ∧ b < a ∨ b < 0 ∧ a < b",
"usedConstants": [
"False",
"Preorder.toLT",
"instHDiv",
"eq_false",
"MulZeroClass.toMul",
"congrAr... | simp [hb, hb.not_gt, one_lt_div_of_neg] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Field.Basic | {
"line": 588,
"column": 4
} | {
"line": 588,
"column": 43
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\n⊢ 1 < a / b ↔ 0 < b ∧ b < a ∨ b < 0 ∧ a < b",
"usedConstants": [
"False",
"Preorder.toLT",
"instHDiv",
"eq_false",
"MulZeroClass.toMul",
"congrAr... | simp [hb, hb.not_gt, one_lt_div_of_neg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Field.Basic | {
"line": 588,
"column": 4
} | {
"line": 588,
"column": 43
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\n⊢ 1 < a / b ↔ 0 < b ∧ b < a ∨ b < 0 ∧ a < b",
"usedConstants": [
"False",
"Preorder.toLT",
"instHDiv",
"eq_false",
"MulZeroClass.toMul",
"congrAr... | simp [hb, hb.not_gt, one_lt_div_of_neg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Perm.Basic | {
"line": 146,
"column": 2
} | {
"line": 147,
"column": 95
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\n⊢ ((fun x1 x2 ↦ x1 = map f x2) ∘r fun x1 x2 ↦ x1 ~ x2) = fun x1 x2 ↦ x1 ~ map f x2",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.map",
"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm._simp_1_1",
"Eq.rec",
"... | conv_rhs => rw [← Relation.comp_eq_fun (map f)]
simp only [← forall₂_eq_eq_eq, forall₂_map_right_iff, forall₂_comp_perm_eq_perm_comp_forall₂] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Perm.Basic | {
"line": 146,
"column": 2
} | {
"line": 147,
"column": 95
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\n⊢ ((fun x1 x2 ↦ x1 = map f x2) ∘r fun x1 x2 ↦ x1 ~ x2) = fun x1 x2 ↦ x1 ~ map f x2",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.map",
"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm._simp_1_1",
"Eq.rec",
"... | conv_rhs => rw [← Relation.comp_eq_fun (map f)]
simp only [← forall₂_eq_eq_eq, forall₂_map_right_iff, forall₂_comp_perm_eq_perm_comp_forall₂] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 48,
"column": 71
} | {
"line": 48,
"column": 79
} | [
{
"pp": "case nil\nM : Type u_4\nN : Type u_5\ninst✝³ : Monoid M\ninst✝² : Monoid N\nl : List M\nF : Type u_8\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhl✝ : l ≠ []\nx : M\nhl : [x] ≠ []\n⊢ (map ⇑f [x]).prod = f [x].prod",
"usedConstants": [
"MulOne.toOne",
"Monoid.toMulOneClass... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 48,
"column": 71
} | {
"line": 48,
"column": 79
} | [
{
"pp": "case cons\nM : Type u_4\nN : Type u_5\ninst✝³ : Monoid M\ninst✝² : Monoid N\nl : List M\nF : Type u_8\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhl✝ : l ≠ []\nhead✝ : M\ntail✝ : List M\ntail_ih✝ : ∀ (x : M), x :: tail✝ ≠ [] → (map (⇑f) (x :: tail✝)).prod = f (x :: tail✝).prod\nx : M\nhl... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 60,
"column": 68
} | {
"line": 60,
"column": 76
} | [
{
"pp": "case nil\nι : Type u_1\nM : Type u_4\nN : Type u_5\nP : Type u_6\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl : List ι\nf : M → N → P\nhf : ∀ (a b : M) (c d : N), f (a * b) (c * d) = f a c * f b d\nf₁ : ι → M\nf₂ : ι → N\nhl✝ : l ≠ []\nx : ι\nhl : [x] ≠ []\n⊢ (map (fun i ↦ f (f₁ i) (f₂ i)... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 60,
"column": 68
} | {
"line": 60,
"column": 76
} | [
{
"pp": "case cons\nι : Type u_1\nM : Type u_4\nN : Type u_5\nP : Type u_6\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl : List ι\nf : M → N → P\nhf : ∀ (a b : M) (c d : N), f (a * b) (c * d) = f a c * f b d\nf₁ : ι → M\nf₂ : ι → N\nhl✝ : l ≠ []\nhead✝ : ι\ntail✝ : List ι\ntail_ih✝ :\n ∀ (x : ι),\... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 152,
"column": 10
} | {
"line": 152,
"column": 13
} | [
{
"pp": "M : Type u_1\ninst✝ : Mul M\na b c D e f : M\nh₁ : a = b\nh₂ : b = c\nh₃ : c = D * e\nh₄ : e = f\n⊢ b = D * f",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"Eq",
"instHMul"
]
}
] | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 360,
"column": 6
} | {
"line": 360,
"column": 15
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nl : NF M\nr : ℕ\nhr : r ≠ 0\nx : M\nhx : x = l.eval\n⊢ x ^ r = (l ^ r).eval",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"congrArg",
"id",
"Int",
"Mathlib.Tactic.FieldSimp.NF.eval_pow",
"Nat.cas... | eval_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Defs | {
"line": 62,
"column": 74
} | {
"line": 62,
"column": 82
} | [
{
"pp": "case e_den\nd : ℕ\nh : d ≠ 0\nw : (Int.natAbs 0).Coprime d\n⊢ d = 1",
"usedConstants": [
"Nat.Coprime",
"congrArg",
"Eq.mp",
"id",
"instOfNatNat",
"Int",
"instOfNat",
"Nat",
"True",
"Int.natAbs",
"eq_self",
"Nat.coprime_zero_le... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Ring.Rat | {
"line": 90,
"column": 61
} | {
"line": 90,
"column": 69
} | [
{
"pp": "q : ℚ\nthis : q.num /. ↑q.den * (↑q.den /. 1) = q.num /. 1\n⊢ q * ↑q.den = ↑q.num",
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"Rat.instMul",
"Rat.num",
"HMul.hMul",
"congrArg",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.divInt",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Ring.Rat | {
"line": 90,
"column": 61
} | {
"line": 90,
"column": 69
} | [
{
"pp": "q : ℚ\nthis : q.num /. ↑q.den * (↑q.den /. 1) = q.num /. 1\n⊢ q * ↑q.den = ↑q.num",
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"Rat.instMul",
"Rat.num",
"HMul.hMul",
"congrArg",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.divInt",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Rat | {
"line": 90,
"column": 61
} | {
"line": 90,
"column": 69
} | [
{
"pp": "q : ℚ\nthis : q.num /. ↑q.den * (↑q.den /. 1) = q.num /. 1\n⊢ q * ↑q.den = ↑q.num",
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"Rat.instMul",
"Rat.num",
"HMul.hMul",
"congrArg",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.divInt",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Field.Rat | {
"line": 97,
"column": 20
} | {
"line": 97,
"column": 50
} | [
{
"pp": "n : ℕ\na : ℚ≥0\n⊢ a ^ ↑n.succ = a ^ ↑n * a",
"usedConstants": [
"Semigroup.toMul",
"HMul.hMul",
"CommSemiring.toSemiring",
"Rat",
"NNRat",
"Int",
"Nat.cast",
"instCommSemiringNNRat",
"Rat.instField",
"HPow.hPow",
"Rat.instNNRatCast",... | by ext; apply Field.zpow_succ' | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.GroupWithZero.Divisibility | {
"line": 89,
"column": 38
} | {
"line": 89,
"column": 70
} | [
{
"pp": "α : Type u_1\ninst✝¹ : CommMonoidWithZero α\ninst✝ : Nontrivial α\nh : IsRelPrime 0 0\n⊢ False",
"usedConstants": [
"not_isRelPrime_zero_zero"
]
}
] | exact not_isRelPrime_zero_zero h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.List.Basic | {
"line": 359,
"column": 27
} | {
"line": 359,
"column": 78
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\nhead✝¹ head✝ c : α\nl : List α\n⊢ (head✝¹ :: head✝ :: c :: l).getLastI = (head✝¹ :: head✝ :: c :: l).getLast?.getD default",
"usedConstants": [
"Inhabited.default",
"List.getLast?",
"List.getLast?_cons_cons",
"congrArg",
"Option.getD",
... | simp [getLastI, getLastI_eq_getLast?_getD (c :: l)] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Basic | {
"line": 359,
"column": 27
} | {
"line": 359,
"column": 78
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\nhead✝¹ head✝ c : α\nl : List α\n⊢ (head✝¹ :: head✝ :: c :: l).getLastI = (head✝¹ :: head✝ :: c :: l).getLast?.getD default",
"usedConstants": [
"Inhabited.default",
"List.getLast?",
"List.getLast?_cons_cons",
"congrArg",
"Option.getD",
... | simp [getLastI, getLastI_eq_getLast?_getD (c :: l)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 359,
"column": 27
} | {
"line": 359,
"column": 78
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\nhead✝¹ head✝ c : α\nl : List α\n⊢ (head✝¹ :: head✝ :: c :: l).getLastI = (head✝¹ :: head✝ :: c :: l).getLast?.getD default",
"usedConstants": [
"Inhabited.default",
"List.getLast?",
"List.getLast?_cons_cons",
"congrArg",
"Option.getD",
... | simp [getLastI, getLastI_eq_getLast?_getD (c :: l)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 860,
"column": 53
} | {
"line": 860,
"column": 61
} | [
{
"pp": "case mp.inl.inl\nα : Type u\nx₁ z₂ : List α\na₂ : α\nnotin_x : ¬a₂ ∈ x₁\nnotin_z : ¬a₂ ∈ z₂\n⊢ x₁ = x₁ ++ [] ∧ a₂ = a₂ ∧ z₂ = z₂",
"usedConstants": [
"congrArg",
"and_self",
"List.append_nil",
"instHAppendOfAppend",
"List",
"And",
"congr",
"True",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.Basic | {
"line": 860,
"column": 53
} | {
"line": 860,
"column": 61
} | [
{
"pp": "case mp.inl.inr\nα : Type u\nx₁ z₂ : List α\na₁ a₂ : α\nnotin_x : ¬a₂ ∈ x₁\nd : List α\nnotin_z : ¬a₂ ∈ d ++ a₂ :: z₂\n⊢ x₁ = x₁ ++ a₁ :: d ∧ a₁ = a₂ ∧ d ++ a₂ :: z₂ = z₂",
"usedConstants": [
"False",
"congrArg",
"true_or",
"False.elim",
"Membership.mem",
"Eq.mp"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.Basic | {
"line": 860,
"column": 53
} | {
"line": 860,
"column": 61
} | [
{
"pp": "case mp.inr.inl\nα : Type u\nx₂ z₁ : List α\na₁ : α\nnotin_z : ¬a₁ ∈ z₁\nnotin_x : ¬a₁ ∈ x₂ ++ []\n⊢ x₂ ++ [] = x₂ ∧ a₁ = a₁ ∧ z₁ = z₁",
"usedConstants": [
"congrArg",
"and_self",
"List.append_nil",
"instHAppendOfAppend",
"List",
"And",
"congr",
"True... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.List.Basic | {
"line": 860,
"column": 53
} | {
"line": 860,
"column": 61
} | [
{
"pp": "case mp.inr.inr\nα : Type u\nx₂ z₁ : List α\na₁ a₂ : α\nnotin_z : ¬a₂ ∈ z₁\nd : List α\nnotin_x : ¬a₂ ∈ x₂ ++ a₂ :: d\n⊢ x₂ ++ a₂ :: d = x₂ ∧ a₁ = a₂ ∧ z₁ = d ++ a₁ :: z₁",
"usedConstants": [
"False",
"congrArg",
"true_or",
"False.elim",
"Membership.mem",
"Eq.mp"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Rat.Lemmas | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 25
} | [
{
"pp": "case mp\nqr : ℚ\n⊢ IsSquare (qr * qr).num ∧ IsSquare (qr * qr).den",
"usedConstants": [
"Eq.mpr",
"Rat.instMul",
"Rat.num",
"HMul.hMul",
"congrArg",
"Rat",
"Rat.den",
"id",
"instMulNat",
"Int",
"Int.instMul",
"And",
"Nat"... | Rat.mul_self_num, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.Ring.Common | {
"line": 661,
"column": 25
} | {
"line": 662,
"column": 35
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na b₁ b₂ c₁ c₂ d : R\nx✝² : a * b₁ = c₁\nx✝¹ : a * b₂ = c₂\nx✝ : c₁ + 0 + c₂ = d\n⊢ a * (b₁ + b₂) = d",
"usedConstants": [
"Distrib.leftDistribClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"CommSemiring... | by
subst_vars; simp [_root_.mul_add] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.GaloisConnection.Basic | {
"line": 236,
"column": 88
} | {
"line": 237,
"column": 43
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\ns : Set β\n⊢ BddAbove (⇑e ⁻¹' s) ↔ BddAbove s",
"usedConstants": [
"Eq.mpr",
"OrderIso.bddAbove_image",
"congrArg",
"Iff.rfl",
"Preorder.toLE",
"id",
"OrderIso",
"BddAbove",
... | by
rw [← e.bddAbove_image, e.image_preimage] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteLattice.Basic | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 10
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝ : SupSet α\np : ι → Prop\nf g : (i : ι) → p i → α\nh : ∀ (i : ι) (hi : p i), f i hi = g i hi\n⊢ ⨆ i, ⨆ (hi : p i), f i hi = ⨆ i, ⨆ (hi : p i), g i hi",
"usedConstants": [
"congrArg",
"iSup",
"funext",
"True",
"eq_self",
"of_eq_tr... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.CompleteLattice.Basic | {
"line": 635,
"column": 2
} | {
"line": 635,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\ns : Set β\nf : β → α\n⊢ sSup (f '' s) = ⨆ a ∈ s, f a",
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"iSup_subtype''",
"Membership.mem",
"Set.Elem",
"id",
"CompleteSemilatticeSup.toSupSet",
... | rw [← iSup_subtype'', sSup_image'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.CompleteLattice.Basic | {
"line": 635,
"column": 2
} | {
"line": 635,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\ns : Set β\nf : β → α\n⊢ sSup (f '' s) = ⨆ a ∈ s, f a",
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"iSup_subtype''",
"Membership.mem",
"Set.Elem",
"id",
"CompleteSemilatticeSup.toSupSet",
... | rw [← iSup_subtype'', sSup_image'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.CompleteLattice.Basic | {
"line": 635,
"column": 2
} | {
"line": 635,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\ns : Set β\nf : β → α\n⊢ sSup (f '' s) = ⨆ a ∈ s, f a",
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"iSup_subtype''",
"Membership.mem",
"Set.Elem",
"id",
"CompleteSemilatticeSup.toSupSet",
... | rw [← iSup_subtype'', sSup_image'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice | {
"line": 739,
"column": 2
} | {
"line": 739,
"column": 37
} | [
{
"pp": "ι : Type u_12\nα : Type u_13\ns : Set ι\nhs : s.Nonempty\nf : ι → Set α\nt : Set α\n⊢ ⋂ i ∈ s, t ∩ f i = t ∩ ⋂ i ∈ s, f i",
"usedConstants": [
"Eq.mpr",
"Set.biInter_inter",
"congrArg",
"Set.iInter",
"Membership.mem",
"id",
"Set.instInter",
"Inter.int... | rw [inter_comm, ← biInter_inter hs] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.CompleteLattice.Basic | {
"line": 742,
"column": 31
} | {
"line": 742,
"column": 71
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\np : β → Type u_8\nf : Sigma p → α\nc : α\n⊢ ⨆ x, f x ≤ c ↔ ⨆ i, ⨆ j, f ⟨i, j⟩ ≤ c",
"usedConstants": [
"congrArg",
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"iSup_le_iff._simp_2",
"LE.le",
"if... | by simp only [iSup_le_iff, Sigma.forall] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 265,
"column": 6
} | {
"line": 267,
"column": 52
} | [
{
"pp": "α : Type u\nι : Sort w\nκ : ι → Sort w'\nminAx : MinimalAxioms α\nf : (a : ι) → κ a → α\nx✝ : CompleteLattice α := minAx.toCompleteLattice\ng : (a : ↑(range fun x ↦ range (f x))) → ↑↑a\n⊢ ⨅ a, ↑(g a) ≤ ⨆ g, ⨅ i, f i (g i)",
"usedConstants": [
"Eq.mpr",
"le_refl",
"iInf",
"co... | refine le_trans ?_ <| le_iSup _ fun a => Classical.choose (g ⟨_, a, rfl⟩).2
refine le_iInf fun a => le_trans (iInf_le _ ⟨range (f a), a, rfl⟩) ?_
rw [← Classical.choose_spec (g ⟨_, a, rfl⟩).2] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 265,
"column": 6
} | {
"line": 267,
"column": 52
} | [
{
"pp": "α : Type u\nι : Sort w\nκ : ι → Sort w'\nminAx : MinimalAxioms α\nf : (a : ι) → κ a → α\nx✝ : CompleteLattice α := minAx.toCompleteLattice\ng : (a : ↑(range fun x ↦ range (f x))) → ↑↑a\n⊢ ⨅ a, ↑(g a) ≤ ⨆ g, ⨅ i, f i (g i)",
"usedConstants": [
"Eq.mpr",
"le_refl",
"iInf",
"co... | refine le_trans ?_ <| le_iSup _ fun a => Classical.choose (g ⟨_, a, rfl⟩).2
refine le_iInf fun a => le_trans (iInf_le _ ⟨range (f a), a, rfl⟩) ?_
rw [← Classical.choose_spec (g ⟨_, a, rfl⟩).2] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 421,
"column": 80
} | {
"line": 423,
"column": 78
} | [
{
"pp": "α : Type u\ninst✝ : Frame α\nι : Type u_1\nι' : Type u_2\nf : ι → α\ng : ι' → α\ns : Set ι\nt : Set ι'\n⊢ (⨆ i ∈ s, f i) ⊓ ⨆ j ∈ t, g j = ⨆ p ∈ s ×ˢ t, f p.1 ⊓ g p.2",
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"Equiv.instEquivLike",
"CompleteLattice.toLattice",
"SP... | by
simp only [iSup_subtype', iSup_inf_iSup]
exact (Equiv.surjective _).iSup_congr (Equiv.Set.prod s t).symm fun x => rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 677,
"column": 6
} | {
"line": 677,
"column": 18
} | [
{
"pp": "α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns : Set α\nhs : s.Nonempty\na : α\n⊢ sSup s ∆ a ≤ sSup ((fun x ↦ x ∆ a) '' s)",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"PartialOrder.toPreorder",
... | sSup_image', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 925,
"column": 34
} | {
"line": 927,
"column": 100
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompletelyDistribLattice β\n⊢ CompletelyDistribLattice α",
"usedConstants": [
"CoheytingAlgebra.toHNot",
"BiheytingAlgebra.toSDiff",
"Equiv.apply_symm_apply",
"Preorder.toLT",
"Lattice.toSemilattic... | by
let completeDistribLattice := e.completeDistribLattice
apply e.injective.completelyDistribLattice <;> intros <;> first | rfl | exact e.apply_symm_apply _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 254,
"column": 51
} | {
"line": 255,
"column": 39
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ Ι a b = Ioc a b ∪ Ioc b a",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Set.union_empty",
"congrArg",
"inf_of_le_left",
"PartialOrder.toPreorder",
"Set.uIoc",
"Preor... | by
cases le_total a b <;> simp [uIoc, *] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.LinearOrder | {
"line": 47,
"column": 53
} | {
"line": 47,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ Ici a \\ Ioi b = Icc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Lattice.toSemilatticeSup",
"Set.Ici",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Dis... | rw [diff_eq, compl_Ioi, Ici_inter_Iic] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Interval.Set.LinearOrder | {
"line": 47,
"column": 53
} | {
"line": 47,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ Ici a \\ Ioi b = Icc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Lattice.toSemilatticeSup",
"Set.Ici",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Dis... | rw [diff_eq, compl_Ioi, Ici_inter_Iic] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.LinearOrder | {
"line": 47,
"column": 53
} | {
"line": 47,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ Ici a \\ Ioi b = Icc a b",
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Lattice.toSemilatticeSup",
"Set.Ici",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Dis... | rw [diff_eq, compl_Ioi, Ici_inter_Iic] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.OrdConnected | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 77
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ↪o β\nhe : (range ⇑e).OrdConnected\nx y : α\n⊢ ⇑e '' Ioo x y = Ioo (e x) (e y)",
"usedConstants": [
"Set.inter_eq_left",
"Iff.mpr",
"Eq.mpr",
"Set.Ioo_subset_Icc_self",
"congrArg",
"Preord... | rw [← e.preimage_Ioo, image_preimage_eq_inter_range,
inter_eq_left.2 <| Ioo_subset_Icc_self.trans <| he.out ⟨_, rfl⟩ ⟨_, rfl⟩] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Interval.Set.OrdConnected | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 77
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ↪o β\nhe : (range ⇑e).OrdConnected\nx y : α\n⊢ ⇑e '' Ioo x y = Ioo (e x) (e y)",
"usedConstants": [
"Set.inter_eq_left",
"Iff.mpr",
"Eq.mpr",
"Set.Ioo_subset_Icc_self",
"congrArg",
"Preord... | rw [← e.preimage_Ioo, image_preimage_eq_inter_range,
inter_eq_left.2 <| Ioo_subset_Icc_self.trans <| he.out ⟨_, rfl⟩ ⟨_, rfl⟩] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.OrdConnected | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 77
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ↪o β\nhe : (range ⇑e).OrdConnected\nx y : α\n⊢ ⇑e '' Ioo x y = Ioo (e x) (e y)",
"usedConstants": [
"Set.inter_eq_left",
"Iff.mpr",
"Eq.mpr",
"Set.Ioo_subset_Icc_self",
"congrArg",
"Preord... | rw [← e.preimage_Ioo, image_preimage_eq_inter_range,
inter_eq_left.2 <| Ioo_subset_Icc_self.trans <| he.out ⟨_, rfl⟩ ⟨_, rfl⟩] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Nonneg.Ring | {
"line": 105,
"column": 4
} | {
"line": 106,
"column": 86
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\n⊢ ∀ (a b c : { x // 0 ≤ x }), a - b ≤ c ↔ a ≤ c + b",
"usedConstants": [
"Lattice.toSemilatticeSup",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"covariant_swap_a... | rintro ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩
simp only [sub_le_iff_le_add, Subtype.mk_le_mk, mk_sub_mk, mk_add_mk, toNonneg_le] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Nonneg.Ring | {
"line": 105,
"column": 4
} | {
"line": 106,
"column": 86
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\n⊢ ∀ (a b c : { x // 0 ≤ x }), a - b ≤ c ↔ a ≤ c + b",
"usedConstants": [
"Lattice.toSemilatticeSup",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"covariant_swap_a... | rintro ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩
simp only [sub_le_iff_le_add, Subtype.mk_le_mk, mk_sub_mk, mk_add_mk, toNonneg_le] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 118,
"column": 8
} | {
"line": 118,
"column": 43
} | [
{
"pp": "case inl\nm n : ℕ\nhn : 1 < n\nh : n ! = m !\nhnm : n < m\n⊢ n = m",
"usedConstants": [
"congrArg",
"Eq.mp",
"instOfNatNat",
"Nat.factorial",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Nat.lt_of_succ_lt",
"Nat.factorial_lt",
"OfNat.ofN... | ← factorial_lt <| lt_of_succ_lt hn, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 122,
"column": 6
} | {
"line": 122,
"column": 41
} | [
{
"pp": "case inr.inr\nm n : ℕ\nhn : 1 < m\nh : n ! = m !\nhnm : m < n\n⊢ n = m",
"usedConstants": [
"congrArg",
"Eq.mp",
"instOfNatNat",
"Nat.factorial",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Nat.lt_of_succ_lt",
"Nat.factorial_lt",
"OfNat... | ← factorial_lt <| lt_of_succ_lt hn, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Lemmas | {
"line": 31,
"column": 26
} | {
"line": 31,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionRing α\np : ℚ\nn : ℕ\n⊢ ↑(p ^ n).num / ↑(p ^ n).den = (↑p.num / ↑p.den) ^ n",
"usedConstants": [
"instPowNat",
"Int.cast",
"Eq.mpr",
"Rat.num",
"instHDiv",
"congrArg",
"Rat.den_pow",
"Rat",
"AddGroupWithOne.toAddMon... | den_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
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