module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Rel | {
"line": 282,
"column": 75
} | {
"line": 282,
"column": 80
} | {
"line": 284,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : SetRel α β\nS : SetRel β γ\nu : Set γ\n⊢ (R ○ S).preimage u = R.preimage (S.preimage u)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"E... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 285,
"column": 68
} | {
"line": 285,
"column": 73
} | {
"line": 287,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\n⊢ ∅.image s = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_self... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 285,
"column": 68
} | {
"line": 285,
"column": 73
} | {
"line": 287,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\n⊢ ∅.image s = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_self... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 285,
"column": 68
} | {
"line": 285,
"column": 73
} | {
"line": 287,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\n⊢ ∅.image s = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_self... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 288,
"column": 74
} | {
"line": 288,
"column": 79
} | {
"line": 290,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\n⊢ ∅.preimage t = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 288,
"column": 74
} | {
"line": 288,
"column": 79
} | {
"line": 290,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\n⊢ ∅.preimage t = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 288,
"column": 74
} | {
"line": 288,
"column": 79
} | {
"line": 290,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\n⊢ ∅.preimage t = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"SetRel",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"iff_s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 290,
"column": 93
} | {
"line": 290,
"column": 98
} | {
"line": 291,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\nhs : s.Nonempty\n⊢ image Set.univ s = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_true... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 290,
"column": 93
} | {
"line": 290,
"column": 98
} | {
"line": 291,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\nhs : s.Nonempty\n⊢ image Set.univ s = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_true... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 290,
"column": 93
} | {
"line": 290,
"column": 98
} | {
"line": 291,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\nhs : s.Nonempty\n⊢ image Set.univ s = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_true... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 7
} | {
"line": 294,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\nht : t.Nonempty\n⊢ preimage Set.univ t = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_t... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 7
} | {
"line": 294,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\nht : t.Nonempty\n⊢ preimage Set.univ t = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 7
} | {
"line": 294,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : Set β\nht : t.Nonempty\n⊢ preimage Set.univ t = Set.univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"and_true",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"iff_t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 294,
"column": 75
} | {
"line": 294,
"column": 80
} | {
"line": 295,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\nh : R.dom ⊆ s\n⊢ R.image s = R.cod",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 294,
"column": 75
} | {
"line": 294,
"column": 80
} | {
"line": 295,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\nh : R.dom ⊆ s\n⊢ R.image s = R.cod",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 294,
"column": 75
} | {
"line": 294,
"column": 80
} | {
"line": 295,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\nh : R.dom ⊆ s\n⊢ R.image s = R.cod",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 295,
"column": 81
} | {
"line": 295,
"column": 86
} | {
"line": 297,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\nh : R.cod ⊆ t\n⊢ R.preimage t = R.dom",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 295,
"column": 81
} | {
"line": 295,
"column": 86
} | {
"line": 297,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\nh : R.cod ⊆ t\n⊢ R.preimage t = R.dom",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 295,
"column": 81
} | {
"line": 295,
"column": 86
} | {
"line": 297,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\nh : R.cod ⊆ t\n⊢ R.preimage t = R.dom",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 298,
"column": 70
} | {
"line": 298,
"column": 75
} | {
"line": 300,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image (s ∩ R.dom) = R.image s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"S... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 298,
"column": 70
} | {
"line": 298,
"column": 75
} | {
"line": 300,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image (s ∩ R.dom) = R.image s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"S... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 298,
"column": 70
} | {
"line": 298,
"column": 75
} | {
"line": 300,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image (s ∩ R.dom) = R.image s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"S... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 301,
"column": 79
} | {
"line": 301,
"column": 84
} | {
"line": 303,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage (t ∩ R.cod) = R.preimage t",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 301,
"column": 79
} | {
"line": 301,
"column": 84
} | {
"line": 303,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage (t ∩ R.cod) = R.preimage t",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 301,
"column": 79
} | {
"line": 301,
"column": 84
} | {
"line": 303,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage (t ∩ R.cod) = R.preimage t",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel.cod",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"id",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 309,
"column": 67
} | {
"line": 309,
"column": 72
} | {
"line": 311,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image s = ⋃ x ∈ s, {y | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.mem... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 309,
"column": 67
} | {
"line": 309,
"column": 72
} | {
"line": 311,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image s = ⋃ x ∈ s, {y | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 309,
"column": 67
} | {
"line": 309,
"column": 72
} | {
"line": 311,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\ns : Set α\n⊢ R.image s = ⋃ x ∈ s, {y | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 311,
"column": 73
} | {
"line": 311,
"column": 78
} | {
"line": 313,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage t = ⋃ y ∈ t, {x | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 311,
"column": 73
} | {
"line": 311,
"column": 78
} | {
"line": 313,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage t = ⋃ y ∈ t, {x | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 311,
"column": 73
} | {
"line": 311,
"column": 78
} | {
"line": 313,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt : Set β\n⊢ R.preimage t = ⋃ y ∈ t, {x | (x, y) ∈ R}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"Iff.of_eq",
"congrArg",
"setOf",
"Set.mem_iUnion._simp_1",
"Membership.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 326,
"column": 66
} | {
"line": 326,
"column": 71
} | {
"line": 328,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt₁ t₂ : Set β\n⊢ R.core (t₁ ∩ t₂) = R.core t₁ ∩ R.core t₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"and_self",
"Membership.mem",
"id",
"Pro... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 326,
"column": 66
} | {
"line": 326,
"column": 71
} | {
"line": 328,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt₁ t₂ : Set β\n⊢ R.core (t₁ ∩ t₂) = R.core t₁ ∩ R.core t₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"and_self",
"Membership.mem",
"id",
"Pro... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 326,
"column": 66
} | {
"line": 326,
"column": 71
} | {
"line": 328,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nt₁ t₂ : Set β\n⊢ R.core (t₁ ∩ t₂) = R.core t₁ ∩ R.core t₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"and_self",
"Membership.mem",
"id",
"Pro... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 330,
"column": 59
} | {
"line": 330,
"column": 64
} | {
"line": 332,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\n⊢ R.core Set.univ = Set.univ",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"Membership.mem",
"Prod.mk",
"SetRel.core",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 330,
"column": 59
} | {
"line": 330,
"column": 64
} | {
"line": 332,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\n⊢ R.core Set.univ = Set.univ",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"Membership.mem",
"Prod.mk",
"SetRel.core",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 330,
"column": 59
} | {
"line": 330,
"column": 64
} | {
"line": 332,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\n⊢ R.core Set.univ = Set.univ",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"Membership.mem",
"Prod.mk",
"SetRel.core",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 333,
"column": 45
} | {
"line": 333,
"column": 50
} | {
"line": 335,
"column": 0
} | [
{
"pp": "β : Type u_2\nt : Set β\n⊢ SetRel.id.core t = t",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel.id",
"SetRel",
"congrArg",
"Membership.mem",
"Prod.mk",
"SetRel.core",
"forall_eq'._simp_1",
"iff_self",
"I... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 333,
"column": 45
} | {
"line": 333,
"column": 50
} | {
"line": 335,
"column": 0
} | [
{
"pp": "β : Type u_2\nt : Set β\n⊢ SetRel.id.core t = t",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel.id",
"SetRel",
"congrArg",
"Membership.mem",
"Prod.mk",
"SetRel.core",
"forall_eq'._simp_1",
"iff_self",
"I... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 333,
"column": 45
} | {
"line": 333,
"column": 50
} | {
"line": 335,
"column": 0
} | [
{
"pp": "β : Type u_2\nt : Set β\n⊢ SetRel.id.core t = t",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel.id",
"SetRel",
"congrArg",
"Membership.mem",
"Prod.mk",
"SetRel.core",
"forall_eq'._simp_1",
"iff_self",
"I... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 64
} | {
"line": 338,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : SetRel α β\nS : SetRel β γ\nu : Set γ\n⊢ (R ○ S).core u = R.core (S.core u)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 64
} | {
"line": 338,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : SetRel α β\nS : SetRel β γ\nu : Set γ\n⊢ (R ○ S).core u = R.core (S.core u)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 64
} | {
"line": 338,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : SetRel α β\nS : SetRel β γ\nu : Set γ\n⊢ (R ○ S).core u = R.core (S.core u)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.RelSeries | {
"line": 221,
"column": 36
} | {
"line": 221,
"column": 58
} | {
"line": 221,
"column": 58
} | [
{
"pp": "α : Type u_1\nr : SetRel α α\ns : RelSeries r\ninst✝ : r.IsIrrefl\n⊢ ¬{x | x ∈ s}.Nontrivial ↔ {x | x ∈ s}.Subsingleton",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"setOf",
"Membership.mem",
"id",
"RelSeries",
"If... | [
"α : Type u_1\nr : SetRel α α\ns : RelSeries r\ninst✝ : r.IsIrrefl\n⊢ {x | x ∈ s}.Subsingleton ↔ {x | x ∈ s}.Subsingleton"
] | Set.not_nontrivial_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.ENat.Lattice | {
"line": 272,
"column": 57
} | {
"line": 273,
"column": 42
} | {
"line": 275,
"column": 0
} | [
{
"pp": "ι : Sort u_2\nf : ι → ℕ∞\na : ℕ∞\n⊢ a + iInf f = ⨅ b, a + f b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"instCompleteLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"instAddENat",
"id",
"Conditionally... | [] | by
rw [add_comm, iInf_add]; simp [add_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rel | {
"line": 510,
"column": 84
} | {
"line": 510,
"column": 89
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nι : Sort u_5\nR✝ R₁✝ R₂✝ : SetRel α β\nS✝ : SetRel β γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ\na✝ a₁ a₂ : α\nb✝ : β\nc✝ : γ\nR R₁ R₂ : SetRel α α\nS : SetRel β β\na b c : α\nx : α × α\nx✝² x✝¹ x✝ : α\n⊢ (x✝², x✝¹) ∈ {x} → (x✝¹, x✝) ∈ {x} → (... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 510,
"column": 84
} | {
"line": 510,
"column": 89
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nι : Sort u_5\nR✝ R₁✝ R₂✝ : SetRel α β\nS✝ : SetRel β γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ\na✝ a₁ a₂ : α\nb✝ : β\nc✝ : γ\nR R₁ R₂ : SetRel α α\nS : SetRel β β\na b c : α\nx : α × α\nx✝² x✝¹ x✝ : α\n⊢ (x✝², x✝¹) ∈ {x} → (x✝¹, x✝) ∈ {x} → (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 510,
"column": 84
} | {
"line": 510,
"column": 89
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nι : Sort u_5\nR✝ R₁✝ R₂✝ : SetRel α β\nS✝ : SetRel β γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ\na✝ a₁ a₂ : α\nb✝ : β\nc✝ : γ\nR R₁ R₂ : SetRel α α\nS : SetRel β β\na b c : α\nx : α × α\nx✝² x✝¹ x✝ : α\n⊢ (x✝², x✝¹) ∈ {x} → (x✝¹, x✝) ∈ {x} → (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 567,
"column": 56
} | {
"line": 567,
"column": 61
} | {
"line": 569,
"column": 0
} | [
{
"pp": "α : Type u_1\n⊢ graph id = SetRel.id",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
"id",
"Eq.refl"
],
"usedFVars": [
"α"
],
"usedGoals": []
}
] | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 567,
"column": 56
} | {
"line": 567,
"column": 61
} | {
"line": 569,
"column": 0
} | [
{
"pp": "α : Type u_1\n⊢ graph id = SetRel.id",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
"id",
"Eq.refl"
],
"usedFVars": [
"α"
],
"usedGoals": []
}
] | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 567,
"column": 56
} | {
"line": 567,
"column": 61
} | {
"line": 569,
"column": 0
} | [
{
"pp": "α : Type u_1\n⊢ graph id = SetRel.id",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
"id",
"Eq.refl"
],
"usedFVars": [
"α"
],
"usedGoals": []
}
] | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 569,
"column": 85
} | {
"line": 569,
"column": 90
} | {
"line": 571,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : β → γ\ng : α → β\n⊢ graph (f ∘ g) = graph g ○ graph f",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Function.graph",
"Function.comp",
"Membership.mem",
"Exis... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 569,
"column": 85
} | {
"line": 569,
"column": 90
} | {
"line": 571,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : β → γ\ng : α → β\n⊢ graph (f ∘ g) = graph g ○ graph f",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Function.graph",
"Function.comp",
"Membership.mem",
"Exis... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 569,
"column": 85
} | {
"line": 569,
"column": 90
} | {
"line": 571,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : β → γ\ng : α → β\n⊢ graph (f ∘ g) = graph g ○ graph f",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Set.ext",
"SetRel",
"congrArg",
"Function.graph",
"Function.comp",
"Membership.mem",
"Exis... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 7
} | {
"line": 580,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α ≃ β\n⊢ Function.graph ⇑f.symm = (Function.graph ⇑f).inv",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"SetRel",
"congrArg",
"Equiv.sy... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 7
} | {
"line": 580,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α ≃ β\n⊢ Function.graph ⇑f.symm = (Function.graph ⇑f).inv",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"SetRel",
"congrArg",
"Equiv.sy... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 7
} | {
"line": 580,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α ≃ β\n⊢ Function.graph ⇑f.symm = (Function.graph ⇑f).inv",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"SetRel",
"congrArg",
"Equiv.sy... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 587,
"column": 20
} | {
"line": 587,
"column": 25
} | {
"line": 587,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\n⊢ ∀ (y : α → β), (fun f ↦ Function.graph f = R) y → y = f",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"SetRel",
"congrArg",
"Function.graph",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 587,
"column": 20
} | {
"line": 587,
"column": 25
} | {
"line": 587,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\n⊢ ∀ (y : α → β), (fun f ↦ Function.graph f = R) y → y = f",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"SetRel",
"congrArg",
"Function.graph",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 587,
"column": 20
} | {
"line": 587,
"column": 25
} | {
"line": 587,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\n⊢ ∀ (y : α → β), (fun f ↦ Function.graph f = R) y → y = f",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"SetRel",
"congrArg",
"Function.graph",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rel | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 9
} | {
"line": 591,
"column": 2
} | [
{
"pp": "case mpr.mp\nα : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\na : α\nb : β\n⊢ (a, b) ∈ Function.graph f → (a, b) ∈ R",
"ppTerm": "?mpr.mp",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Rel | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 9
} | {
"line": 591,
"column": 2
} | [
{
"pp": "case mpr.mp\nα : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\na : α\nb : β\n⊢ (a, b) ∈ Function.graph f → (a, b) ∈ R",
"ppTerm": "?mpr.mp",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rel | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 9
} | {
"line": 591,
"column": 2
} | [
{
"pp": "case mpr.mp\nα : Type u_1\nβ : Type u_2\nR : SetRel α β\nh : ∀ (a : α), ∃! b, (a, b) ∈ R\nf : α → β\nhf : ∀ (x : α), (x, f x) ∈ R\na : α\nb : β\n⊢ (a, b) ∈ Function.graph f → (a, b) ∈ R",
"ppTerm": "?mpr.mp",
"assigned": true,
"usedConstants": [
"SetRel",
"Function.graph",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.RelSeries | {
"line": 415,
"column": 6
} | {
"line": 415,
"column": 21
} | {
"line": 416,
"column": 6
} | [
{
"pp": "case e'_3\nα : Type u_1\nr : SetRel α α\nβ : Type u_2\ns : SetRel β β\np : RelSeries r\ni : Fin p.length\na : α\nprev_connect : (p.toFun i.castSucc, a) ∈ r\nconnect_next : (a, p.toFun i.succ) ∈ r\nm : Fin (p.length + 1)\nx : α := i.succ.castSucc.insertNth a p.toFun m.castSucc\ny : α := i.succ.castSucc.... | [
"case e'_4\nα : Type u_1\nr : SetRel α α\nβ : Type u_2\ns : SetRel β β\np : RelSeries r\ni : Fin p.length\na : α\nprev_connect : (p.toFun i.castSucc, a) ∈ r\nconnect_next : (a, p.toFun i.succ) ∈ r\nm : Fin (p.length + 1)\nx : α := i.succ.castSucc.insertNth a p.toFun m.castSucc\ny : α := i.succ.castSucc.insertNth a ... | · ext; exact hm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.RelSeries | {
"line": 420,
"column": 6
} | {
"line": 420,
"column": 26
} | {
"line": 421,
"column": 6
} | [
{
"pp": "case inr.inr\nα : Type u_1\nr : SetRel α α\nβ : Type u_2\ns : SetRel β β\np : RelSeries r\ni : Fin p.length\na : α\nprev_connect : (p.toFun i.castSucc, a) ∈ r\nconnect_next : (a, p.toFun i.succ) ∈ r\nm : Fin (p.length + 1)\nx : α := i.succ.castSucc.insertNth a p.toFun m.castSucc\ny : α := i.succ.castSu... | [
"case inr.inr.inl\nα : Type u_1\nr : SetRel α α\nβ : Type u_2\ns : SetRel β β\np : RelSeries r\ni : Fin p.length\na : α\nprev_connect : (p.toFun i.castSucc, a) ∈ r\nconnect_next : (a, p.toFun i.succ) ∈ r\nm : Fin (p.length + 1)\nx : α := i.succ.castSucc.insertNth a p.toFun m.castSucc\ny : α := i.succ.castSucc.inser... | obtain hm | hm := hm | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Order.RelSeries | {
"line": 424,
"column": 10
} | {
"line": 424,
"column": 15
} | {
"line": 425,
"column": 8
} | [
{
"pp": "case e'_3\nα : Type u_1\nr : SetRel α α\nβ : Type u_2\ns : SetRel β β\np : RelSeries r\ni : Fin p.length\na : α\nprev_connect : (p.toFun i.castSucc, a) ∈ r\nconnect_next : (a, p.toFun i.succ) ∈ r\nm : Fin (p.length + 1)\nx : α := i.succ.castSucc.insertNth a p.toFun m.castSucc\ny : α := i.succ.castSucc.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Exact.Basic | {
"line": 478,
"column": 2
} | {
"line": 479,
"column": 57
} | {
"line": 480,
"column": 2
} | [
{
"pp": "R : Type u_8\nM : Type u_9\nN : Type u_10\nP : Type u_11\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup N\ninst✝³ : AddCommGroup P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N\ng : N →ₗ[R] P\nh : Exact ⇑f ⇑g\nhf : Injective ⇑f\nhg : Surjective ⇑g\nt... | [
"R : Type u_8\nM : Type u_9\nN : Type u_10\nP : Type u_11\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup N\ninst✝³ : AddCommGroup P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N\ng : N →ₗ[R] P\nh : Exact ⇑f ⇑g\nhf : Injective ⇑f\nhg : Surjective ⇑g\ntfae_1_iff_3 ... | tfae_have 2 ↔ 3 := by
simpa using (h.splitInjectiveEquiv hg).nonempty_congr | Mathlib.Tactic.TFAE._aux_Mathlib_Tactic_TFAE___macroRules_Mathlib_Tactic_TFAE_tfaeHave_1 | Mathlib.Tactic.TFAE.tfaeHave |
Mathlib.Algebra.Exact.Basic | {
"line": 489,
"column": 2
} | {
"line": 491,
"column": 20
} | {
"line": 493,
"column": 0
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R M\ninst✝ : Module R N\n⊢ Exact ⇑(LinearMap.inr R M N) ⇑(LinearMap.fst R M N)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"LinearMap.fst",
... | [] | rintro ⟨x, y⟩
simp only [LinearMap.fst_apply, @eq_comm _ x, LinearMap.coe_inr, Set.mem_range, Prod.mk.injEq,
exists_eq_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Exact.Basic | {
"line": 489,
"column": 2
} | {
"line": 491,
"column": 20
} | {
"line": 493,
"column": 0
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R M\ninst✝ : Module R N\n⊢ Exact ⇑(LinearMap.inr R M N) ⇑(LinearMap.fst R M N)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"LinearMap.fst",
... | [] | rintro ⟨x, y⟩
simp only [LinearMap.fst_apply, @eq_comm _ x, LinearMap.coe_inr, Set.mem_range, Prod.mk.injEq,
exists_eq_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Exact.Basic | {
"line": 516,
"column": 6
} | {
"line": 516,
"column": 16
} | {
"line": 516,
"column": 17
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_6\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup N\ninst✝³ : AddCommGroup P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N\ng : N →ₗ[R] P\nhfg : Exact ⇑f ⇑g\np : Submodule R M\nq : Submodule R N\nr : Su... | [
"R : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_6\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup N\ninst✝³ : AddCommGroup P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N\ng : N →ₗ[R] P\nhfg : Exact ⇑f ⇑g\np : Submodule R M\nq : Submodule R N\nr : Submodule R P\... | exact_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.KrullDimension | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 29
} | {
"line": 145,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na : α\nn : ℕ∞\nh : ∀ (p : LTSeries α), RelSeries.last p = a → ↑p.length ≤ n\np : LTSeries α\nhlast : RelSeries.last p ≤ a\n⊢ ↑p.length ≤ n",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"RelSeries.last",
"ENat.i... | [
"case inr\nα : Type u_1\ninst✝ : Preorder α\na : α\nn : ℕ∞\nh : ∀ (p : LTSeries α), RelSeries.last p = a → ↑p.length ≤ n\np : LTSeries α\nhlast : RelSeries.last p ≤ a\nthis :\n ∀ {α : Type u_1} [inst : Preorder α] {a : α} {n : ℕ∞},\n (∀ (p : LTSeries α), RelSeries.last p = a → ↑p.length ≤ n) →\n ∀ ⦃p : LTS... | wlog hlenpos : p.length ≠ 0 | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.LinearAlgebra.TensorProduct.Defs | {
"line": 156,
"column": 42
} | {
"line": 156,
"column": 82
} | {
"line": 156,
"column": 82
} | [
{
"pp": "R : Type u_1\nR₂ : Type u_2\nR₃ : Type u_3\nR' : Type u_4\nR'' : Type u_5\ninst✝³⁵ : CommSemiring R\ninst✝³⁴ : CommSemiring R₂\ninst✝³³ : CommSemiring R₃\ninst✝³² : Monoid R'\ninst✝³¹ : Semiring R''\nσ₁₂ : R →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R →+* R₃\nA : Type u_6\nM : Type u_7\nN : Type u_8\nP : Type u_9... | [] | by rw [Subsingleton.elim x 0, zero_tmul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.KrullDimension | {
"line": 1012,
"column": 4
} | {
"line": 1012,
"column": 31
} | {
"line": 1013,
"column": 4
} | [
{
"pp": "case a\nα : Type u_1\ninst✝ : Preorder α\nx : α\np : LTSeries (WithBot α)\nhlast : RelSeries.last p = ↑x\n⊢ ↑p.length ≤ height x + 1",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"Preorder.toLT",
"ins... | [
"case a.inr\nα : Type u_1\ninst✝ : Preorder α\nx : α\np : LTSeries (WithBot α)\nhlast : RelSeries.last p = ↑x\nthis :\n ∀ {α : Type u_1} [inst : Preorder α] (x : α) (p : LTSeries (WithBot α)),\n RelSeries.last p = ↑x → p.length ≠ 0 → ↑p.length ≤ height x + 1\nhlenpos : ¬p.length ≠ 0\n⊢ ↑p.length ≤ height x + 1"... | wlog hlenpos : p.length ≠ 0 | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.LinearAlgebra.TensorProduct.Defs | {
"line": 393,
"column": 25
} | {
"line": 393,
"column": 30
} | {
"line": 395,
"column": 0
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝⁵ : CommSemiring R\nN : Type u_8\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\nι : Type u_22\ninst✝² : DecidableEq ι\nM : ι → Type u_23\ninst✝¹ : (i : ι) → AddCommMonoid (M i)\ninst✝ : (i : ι) → Module R (M i)\ni : ι\nx : N\nm : M i\nj : ι\nh : i = j\n⊢ x ⊗ₜ[R] Pi.single ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.TensorProduct.Defs | {
"line": 393,
"column": 25
} | {
"line": 393,
"column": 30
} | {
"line": 395,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝⁵ : CommSemiring R\nN : Type u_8\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\nι : Type u_22\ninst✝² : DecidableEq ι\nM : ι → Type u_23\ninst✝¹ : (i : ι) → AddCommMonoid (M i)\ninst✝ : (i : ι) → Module R (M i)\ni : ι\nx : N\nm : M i\nj : ι\nh : ¬i = j\n⊢ x ⊗ₜ[R] Pi.single... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.TensorProduct.Defs | {
"line": 398,
"column": 25
} | {
"line": 398,
"column": 30
} | {
"line": 400,
"column": 0
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝⁵ : CommSemiring R\nN : Type u_8\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\nι : Type u_22\ninst✝² : DecidableEq ι\nM : ι → Type u_23\ninst✝¹ : (i : ι) → AddCommMonoid (M i)\ninst✝ : (i : ι) → Module R (M i)\ni : ι\nx : N\nm : M i\nj : ι\nh : i = j\n⊢ Pi.single i m j ⊗ₜ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.TensorProduct.Defs | {
"line": 398,
"column": 25
} | {
"line": 398,
"column": 30
} | {
"line": 400,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝⁵ : CommSemiring R\nN : Type u_8\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\nι : Type u_22\ninst✝² : DecidableEq ι\nM : ι → Type u_23\ninst✝¹ : (i : ι) → AddCommMonoid (M i)\ninst✝ : (i : ι) → Module R (M i)\ni : ι\nx : N\nm : M i\nj : ι\nh : ¬i = j\n⊢ Pi.single i m j ⊗... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Module.Submodule.Finsupp | {
"line": 92,
"column": 76
} | {
"line": 92,
"column": 81
} | {
"line": 92,
"column": 81
} | [
{
"pp": "α : Type u_1\nR : Type u_2\nM : Type u_3\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_4\ninst✝² : Monoid S\ninst✝¹ : DistribMulAction S M\nsR : Set R\ns✝ : Set S\nN : Submodule R M\ninst✝ : SMulCommClass R R M\ns t : Set R\nx : Submodule R M\nn✝ : M\nw✝¹ : R\nleft✝¹ :... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.Coprime.Basic | {
"line": 53,
"column": 12
} | {
"line": 53,
"column": 28
} | {
"line": 53,
"column": 28
} | [
{
"pp": "R : Type u\ninst✝ : CommSemiring R\nx y : R\nH✝ : IsCoprime x y\na b : R\nH : a * x + b * y = 1\n⊢ b * y + a * x = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"CommSem... | [] | rw [add_comm, H] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Coprime.Basic | {
"line": 53,
"column": 12
} | {
"line": 53,
"column": 28
} | {
"line": 53,
"column": 28
} | [
{
"pp": "R : Type u\ninst✝ : CommSemiring R\nx y : R\nH✝ : IsCoprime x y\na b : R\nH : a * x + b * y = 1\n⊢ b * y + a * x = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"CommSem... | [] | rw [add_comm, H] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Coprime.Basic | {
"line": 53,
"column": 12
} | {
"line": 53,
"column": 28
} | {
"line": 53,
"column": 28
} | [
{
"pp": "R : Type u\ninst✝ : CommSemiring R\nx y : R\nH✝ : IsCoprime x y\na b : R\nH : a * x + b * y = 1\n⊢ b * y + a * x = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"CommSem... | [] | rw [add_comm, H] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Coprime.Basic | {
"line": 432,
"column": 2
} | {
"line": 432,
"column": 25
} | {
"line": 433,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\ninst✝¹ : LinearOrder R\ninst✝ : AddLeftMono R\nx y : R\nx✝ : 0 ≤ x ∨ x < 0\n⊢ IsCoprime |x| y ↔ IsCoprime x y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"P... | [] | cases le_or_gt 0 x with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.Coprime.Lemmas | {
"line": 147,
"column": 39
} | {
"line": 147,
"column": 56
} | {
"line": 147,
"column": 56
} | [
{
"pp": "case pos\nR : Type u\nI : Type v\ninst✝¹ : CommSemiring R\ns : I → R\nt✝ : Finset I\ninst✝ : DecidableEq I\na : I\nt : Finset I\nhat : a ∉ t\nh : t.Nonempty\nih : (∃ μ, ∑ i ∈ t, μ i * ∏ j ∈ t \\ {i}, s j = 1) ↔ Pairwise (IsCoprime on fun i ↦ s ↑i)\nmem : ∀ x ∈ t, a ∈ insert a t \\ {x}\nμ : I → R\nhμ✝ :... | [
"case pos\nR : Type u\nI : Type v\ninst✝¹ : CommSemiring R\ns : I → R\nt✝ : Finset I\ninst✝ : DecidableEq I\na : I\nt : Finset I\nhat : a ∉ t\nh : t.Nonempty\nih : (∃ μ, ∑ i ∈ t, μ i * ∏ j ∈ t \\ {i}, s j = 1) ↔ Pairwise (IsCoprime on fun i ↦ s ↑i)\nmem : ∀ x ∈ t, a ∈ insert a t \\ {x}\nμ : I → R\nhμ✝ : μ a * s (Ex... | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Algebra.Operations | {
"line": 378,
"column": 63
} | {
"line": 378,
"column": 68
} | {
"line": 378,
"column": 68
} | [
{
"pp": "R : Type u\ninst✝⁴ : Semiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\ninst✝ : IsReduced A\nM : Submodule R A\nn : ℕ\nhn : n ≠ 0\n⊢ M = ⊥ → M ^ n = ⊥",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Submodule",
"False",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Algebra.Operations | {
"line": 378,
"column": 63
} | {
"line": 378,
"column": 68
} | {
"line": 378,
"column": 68
} | [
{
"pp": "R : Type u\ninst✝⁴ : Semiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\ninst✝ : IsReduced A\nM : Submodule R A\nn : ℕ\nhn : n ≠ 0\n⊢ M = ⊥ → M ^ n = ⊥",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Submodule",
"False",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Algebra.Operations | {
"line": 378,
"column": 63
} | {
"line": 378,
"column": 68
} | {
"line": 378,
"column": 68
} | [
{
"pp": "R : Type u\ninst✝⁴ : Semiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\ninst✝ : IsReduced A\nM : Submodule R A\nn : ℕ\nhn : n ≠ 0\n⊢ M = ⊥ → M ^ n = ⊥",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Submodule",
"False",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Coprime.Lemmas | {
"line": 207,
"column": 85
} | {
"line": 210,
"column": 50
} | {
"line": 212,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : CommSemiring R\nx y : R\nm : ℕ\nhm : 0 < m\n⊢ IsCoprime (x ^ m) y ↔ IsCoprime x y",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"IsCoprime.pow_left",
"Iff.mpr",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"Finset.card_... | [] | by
refine ⟨fun h ↦ ?_, IsCoprime.pow_left⟩
rw [← Finset.card_range m, ← Finset.prod_const] at h
exact h.of_prod_left 0 (Finset.mem_range.mpr hm) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Algebra.Operations | {
"line": 548,
"column": 74
} | {
"line": 555,
"column": 12
} | {
"line": 557,
"column": 0
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Mul A\ninst✝ : Module R A\nS S' : Set A\nx : A\nhx : x ∈ span R (S * S')\n⊢ ∃ T T', ↑T ⊆ S ∧ ↑T' ⊆ S' ∧ x ∈ span R (↑T * ↑T')",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | by
classical
obtain ⟨U, h, hU⟩ := mem_span_finite_of_mem_span hx
obtain ⟨T, T', hS, hS', h⟩ := Finset.subset_mul h
use T, T', hS, hS'
have h' : (U : Set A) ⊆ T * T' := by assumption_mod_cast
have h'' := span_mono h' hU
assumption | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Ideal.Prod | {
"line": 82,
"column": 6
} | {
"line": 82,
"column": 15
} | {
"line": 82,
"column": 15
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal R\nJ : Ideal S\nx : R × S\nh : x ∈ I.prod J\n⊢ (RingHom.fst R S) x ∈ I",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Submodule",
"Semiring.toModule",
"RingHom",
"Membership.mem",
... | [] | exact h.1 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Algebra.Operations | {
"line": 764,
"column": 2
} | {
"line": 764,
"column": 69
} | {
"line": 766,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝³ : CommSemiring R\nA : Type v\ninst✝² : Semiring A\ninst✝¹ : Algebra R A\ninst✝ : FaithfulSMul R A\n⊢ (Units.map ↑(spanSingleton R)).ker = (Units.map ↑(algebraMap R A)).range",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
... | [] | ext; simpa [Units.ext_iff, eq_comm] using span_singleton_eq_one_iff | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Algebra.Operations | {
"line": 764,
"column": 2
} | {
"line": 764,
"column": 69
} | {
"line": 766,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝³ : CommSemiring R\nA : Type v\ninst✝² : Semiring A\ninst✝¹ : Algebra R A\ninst✝ : FaithfulSMul R A\n⊢ (Units.map ↑(spanSingleton R)).ker = (Units.map ↑(algebraMap R A)).range",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
... | [] | ext; simpa [Units.ext_iff, eq_comm] using span_singleton_eq_one_iff | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Ideal.Prod | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 67
} | {
"line": 170,
"column": 0
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal S\nh : (⊤.prod I).IsPrime\n⊢ (map (↑RingEquiv.prodComm) (⊤.prod I)).IsPrime",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"Prod.instMul",
"Prod.instAdd",
"Ring... | [] | exact map_isPrime_of_equiv (RingEquiv.prodComm (R := R) (S := S)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.Ideal.Prod | {
"line": 184,
"column": 69
} | {
"line": 184,
"column": 78
} | {
"line": 184,
"column": 78
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal R\nJ : Ideal S\nx✝¹ : 1 ∉ I ∧ 1 ∉ J\nx✝ : 1 ∉ I.prod J\nhI : 1 ∉ I\nhJ : 1 ∉ J\n⊢ (1, 0) ∉ I.prod J",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Fa... | [] | simp [hI] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Ideal.Prod | {
"line": 184,
"column": 69
} | {
"line": 184,
"column": 78
} | {
"line": 184,
"column": 78
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal R\nJ : Ideal S\nx✝¹ : 1 ∉ I ∧ 1 ∉ J\nx✝ : 1 ∉ I.prod J\nhI : 1 ∉ I\nhJ : 1 ∉ J\n⊢ (1, 0) ∉ I.prod J",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Fa... | [] | simp [hI] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Ideal.Prod | {
"line": 184,
"column": 69
} | {
"line": 184,
"column": 78
} | {
"line": 184,
"column": 78
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal R\nJ : Ideal S\nx✝¹ : 1 ∉ I ∧ 1 ∉ J\nx✝ : 1 ∉ I.prod J\nhI : 1 ∉ I\nhJ : 1 ∉ J\n⊢ (1, 0) ∉ I.prod J",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Fa... | [] | simp [hI] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Algebra.Operations | {
"line": 884,
"column": 77
} | {
"line": 885,
"column": 25
} | {
"line": 887,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nI J K : Submodule R A\n⊢ I ≤ J / K ↔ I * K ≤ J",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"instHDiv",
"HMul.hMul",
"IsScalarTowe... | [] | by
rw [le_div_iff, mul_le] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Ideal.Maps | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 76
} | {
"line": 55,
"column": 4
} | [
{
"pp": "R : Type u\nS : Type v\nF : Type u_1\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : FunLike F R S\nf : F\nI✝ J : Ideal R\nK L : Ideal S\ninst✝ : RingHomClass F R S\nI : Ideal S\nc x : R\nhx : x ∈ ⇑f ⁻¹' ↑I\n⊢ c • x ∈ ⇑f ⁻¹' ↑I",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
... | [
"R : Type u\nS : Type v\nF : Type u_1\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : FunLike F R S\nf : F\nI✝ J : Ideal R\nK L : Ideal S\ninst✝ : RingHomClass F R S\nI : Ideal S\nc x : R\nhx : f x ∈ I\n⊢ f c * f x ∈ I"
] | simp only [smul_eq_mul, Set.mem_preimage, map_mul, SetLike.mem_coe] at * | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.EuclideanDomain.Basic | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 58
} | {
"line": 83,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : EuclideanDomain R\na : R\na0 : ¬a = 0\n⊢ 0 / a = 0",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"Eq.mp",
... | [] | simpa only [zero_mul] using mul_div_cancel_right₀ 0 a0 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.EuclideanDomain.Basic | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 58
} | {
"line": 83,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : EuclideanDomain R\na : R\na0 : ¬a = 0\n⊢ 0 / a = 0",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"Eq.mp",
... | [] | simpa only [zero_mul] using mul_div_cancel_right₀ 0 a0 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.EuclideanDomain.Basic | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 58
} | {
"line": 83,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : EuclideanDomain R\na : R\na0 : ¬a = 0\n⊢ 0 / a = 0",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"Eq.mp",
... | [] | simpa only [zero_mul] using mul_div_cancel_right₀ 0 a0 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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