module large_stringlengths 16 84 | split large_stringclasses 1
value | const float64 | goal large_stringlengths 7 160k | type large_stringlengths 1 123k | name large_stringlengths 1 85 | removals listlengths 0 28 | tactic large_stringlengths 1 8.8k | kind large_stringclasses 2
values | roundtrip float64 | success float64 | used float64 | usedTactic float64 | typeFromPp float64 | messages listlengths 2 2 | tools listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommMagma G
inst_2 : Add H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
⊢ (f : (a : G) → H) (a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b | (f : (a : G) → H) (x + a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b | rw | [] | rw [add_comm, map_add_const] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommMagma G\ninst_2 : Add H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\n⊢ (f : (a : G) → H) (a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b\n```\n... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommMagma G
inst_2 : Add H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
rw : (f : (a : G) → H) (x + a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b
⊢ (f : (a : G) → H) (a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b | HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b | rw₁ | [] | rw [add_comm, map_add_const] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommMagma G\ninst_2 : Add H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nrw : (f : (a : G) → H) (x + a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) b\n⊢ ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommMonoid G
inst_2 : AddMonoid H
inst_3 : AddConstMapClass F G H a b
f : F
n : ℕ
x : G
⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | rw | [] | rw [add_comm, map_add_nsmul] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommMonoid G\ninst_2 : AddMonoid H\ninst_3 : AddConstMapClass F G H a b\nf : F\nn : ℕ\nx : G\n⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f : (a : G) → ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommMonoid G
inst_2 : AddMonoid H
inst_3 : AddConstMapClass F G H a b
f : F
n : ℕ
x : G
rw : (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b)
⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f :... | HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | rw₁ | [] | rw [add_comm, map_add_nsmul] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommMonoid G\ninst_2 : AddMonoid H\ninst_3 : AddConstMapClass F G H a b\nf : F\nn : ℕ\nx : G\nrw : (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G)... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
n : ℕ
| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | ((f : (a : G) → H) (x - n • a) : H) | rw | [] | rw [← sub_add_cancel x (n • a), map_add_nsmul, add_sub_cancel_right] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b)\n```\n\nLibrary theo... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
n : ℕ
| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | ((f : (a : G) → H) (x - n • a) : H) | rw | [] | rw [← sub_add_cancel x (n • a), map_add_nsmul, add_sub_cancel_right] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b)\n```\n\nLibrary theo... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
n : ℕ
| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | ((f : (a : G) → H) (x - n • a) : H) | rw | [] | rw [← sub_add_cancel x (n • a), map_add_nsmul, add_sub_cancel_right] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n| HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b)\n```\n\nLibrary theo... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
n : ℕ
⊢ (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | conv_rhs | [] | conv_rhs => rw [← sub_add_cancel x (n • a), map_add_nsmul, add_sub_cancel_right] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n⊢ (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f : (a : G) → H) x :... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
x : G
n : ℕ
conv_rhs : (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b)
⊢ (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f :... | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x - n • a) : H) ((f : (a : G) → H) (x - n • a) : H) | conv_rhs₁ | [] | conv_rhs => rw [← sub_add_cancel x (n • a), map_add_nsmul, add_sub_cancel_right] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\nconv_rhs : (f : (a : G) → H) (x - n • a) = HSub.hSub (α := H) ((f : (a : G)... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
x : G
n : ℤ
⊢ (f : (a : G) → H) (x + (↑n : G)) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x + (↑n : G)) : H) ((f : (a : G) → H) (x + HSMul.hSMul (β := G) n 1) : H) | rw | [] | rw [← map_add_zsmul f x n, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℤ\n⊢ (f : (a : G) → H) (x + (↑n : G)) = HAdd.hAdd (α := H) ((f : (a : G) → H) ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
x : G
n : ℤ
rw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x + (↑n : G)) : H) ((f : (a : G) → H) (x + HSMul.hSMul (β := G) n 1) : H)
⊢ (f : (a : G) → H) (x + (↑n : G... | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x + (↑n : G)) : H) ((f : (a : G) → H) (x + (↑n : G)) : H) | rw₁ | [] | rw [← map_add_zsmul f x n, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℤ\nrw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x + (↑n : G)) : H) ((f : (a ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
x : G
n : ℤ
⊢ (f : (a : G) → H) (x - (↑n : G)) = HSub.hSub (α := H) ((f : (a : G) → H) x : H) (n • b) | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x - (↑n : G)) : H) ((f : (a : G) → H) (x - HSMul.hSMul (β := G) n 1) : H) | rw | [] | rw [← map_sub_zsmul, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℤ\n⊢ (f : (a : G) → H) (x - (↑n : G)) = HSub.hSub (α := H) ((f : (a : G) → H) ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
x : G
n : ℤ
rw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x - (↑n : G)) : H) ((f : (a : G) → H) (x - HSMul.hSMul (β := G) n 1) : H)
⊢ (f : (a : G) → H) (x - (↑n : G... | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x - (↑n : G)) : H) ((f : (a : G) → H) (x - (↑n : G)) : H) | rw₁ | [] | rw [← map_sub_zsmul, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℤ\nrw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) (x - (↑n : G)) : H) ((f : (a ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
n : ℤ
x : G
⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | rw | [] | rw [add_comm, map_add_zsmul] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nn : ℤ\nx : G\n⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f : (a : G) → H)... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H a b
f : F
n : ℤ
x : G
rw : (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b)
⊢ (f : (a : G) → H) (n • a + x) = HAdd.hAdd (α := H) ((f : (... | HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | rw₁ | [] | rw [add_comm, map_add_zsmul] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H a b\nf : F\nn : ℤ\nx : G\nrw : (f : (a : G) → H) (x + n • a) = HAdd.hAdd (α := H) ((f : (a : G) →... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddCommGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
n : ℤ
x : G
⊢ (f : (a : G) → H) ((↑n : G) + x) = HAdd.hAdd (α := H) ((f : (a : G) → H) x : H) (n • b) | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) ((↑n : G) + x) : H) ((f : (a : G) → H) (HSMul.hSMul (β := G) n 1 + x) : H) | rw | [] | rw [← map_zsmul_add, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddCommGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nn : ℤ\nx : G\n⊢ (f : (a : G) → H) ((↑n : G) + x) = HAdd.hAdd (α := H) ((f : (a : G) →... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
b : H
inst_1 : AddCommGroupWithOne G
inst_2 : AddGroup H
inst_3 : AddConstMapClass F G H 1 b
f : F
n : ℤ
x : G
rw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) ((↑n : G) + x) : H) ((f : (a : G) → H) (HSMul.hSMul (β := G) n 1 + x) : H)
⊢ (f : (a : G) → H) ((↑n : G... | Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) ((↑n : G) + x) : H) ((f : (a : G) → H) ((↑n : G) + x) : H) | rw₁ | [] | rw [← map_zsmul_add, zsmul_one] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\nb : H\ninst_1 : AddCommGroupWithOne G\ninst_2 : AddGroup H\ninst_3 : AddConstMapClass F G H 1 b\nf : F\nn : ℤ\nx : G\nrw : Eq.{u_3 + 1} (α := H) ((f : (a : G) → H) ((↑n : G) + x) : H) ((f :... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
hR : CovariantClass H H (fun (x y : H) ↦ y + x) ... | ∀ (hR : Covariant H H (fun (x y : H) ↦ y + x) R), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | replace | [
"hR"
] | replace hR := hR.elim | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | 0 ≤ a | ha' | [] | have ha' : 0 ≤ a := ha.le | hypothesis | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (this : ∀ (x y : G) (hxy : x < y) (hx : x ∈ Ico l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y))
(hx : x ∉ Ico l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | inr | [] | wlog hx : x ∈ Ico l (l + a) generalizing x y | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (x y : G) (hxy : x < y) (hx : x ∈ Ico l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | wlog | [
"x",
"y",
"hxy"
] | wlog hx : x ∈ Ico l (l + a) generalizing x y | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (m : ℤ) (hm : x - m • a ∈ Ico l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | inr | [] | rcases existsUnique_sub_zsmul_mem_Ico ha x l with ⟨m, hm, -⟩ | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | R ((f : (a : G) → H) (x - m • a)) ((f : (a : G) → H) (y - m • a)) | inr | [] | suffices R (f (x - m • a)) (f (y - m • a)) by simpa using hR (m • b) this | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (n : ℤ) (hny : y - n • a ∈ Ioc l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | rcases | [] | rcases existsUnique_sub_zsmul_mem_Ioc ha y l with ⟨n, hny, -⟩ | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hn : n < 0), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | inl | [] | rcases lt_trichotomy n 0 with hn | rfl | hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hny : y - HSMul.hSMul (α := ℤ) 0 a ∈ Ioc l (l + a)), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | inr | [
"n",
"hny"
] | rcases lt_trichotomy n 0 with hn | rfl | hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hn : 0 < n), R ((f : (a : G) → H) x) ((f : (a : G) → H) y) | inr₁ | [] | rcases lt_trichotomy n 0 with hn | rfl | hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | y ≤ x | inl | [] | refine absurd ?_ hxy.not_ge | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + a + n • a = l + (1 + n) • a | rw | [] | rw [add_comm n, add_smul, one_smul, add_assoc] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + a + n • a = l + (HSMul.hSMul (α := ℤ) 1 a + n • a) | rw₁ | [] | rw [add_comm n, add_smul, one_smul, add_assoc] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + a + n • a = l + (a + n • a) | rw₂ | [] | rw [add_comm n, add_smul, one_smul, add_assoc] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + (a + n • a) = l + (a + n • a) | rw₃ | [] | rw [add_comm n, add_smul, one_smul, add_assoc] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | n + 1 ≤ 0 | bc | [] | gcongr | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + a + n • a = l + (n + 1) • a | y₁ | [] | calc
y ≤ l + a + n • a := sub_le_iff_le_add.1 hny.2
_ = l + (n + 1) • a := by rw [add_comm n, add_smul, one_smul, add_assoc]
_ ≤ l + (0 : ℤ) • a := by gcongr; lia
_ ≤ x := by simpa using hx.1 | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + (n + 1) • a ≤ l + HSMul.hSMul (α := ℤ) 0 a | y₂ | [] | calc
y ≤ l + a + n • a := sub_le_iff_le_add.1 hny.2
_ = l + (n + 1) • a := by rw [add_comm n, add_smul, one_smul, add_assoc]
_ ≤ l + (0 : ℤ) • a := by gcongr; lia
_ ≤ x := by simpa using hx.1 | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l + HSMul.hSMul (α := ℤ) 0 a ≤ x | y₃ | [] | calc
y ≤ l + a + n • a := sub_le_iff_le_add.1 hny.2
_ = l + (n + 1) • a := by rw [add_comm n, add_smul, one_smul, add_assoc]
_ ≤ l + (0 : ℤ) • a := by gcongr; lia
_ ≤ x := by simpa using hx.1 | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | R ((f : (a : G) → H) x) ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) | trans | [] | trans f (l + (1 : ℤ) • a) | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) y) | trans₁ | [] | trans f (l + (1 : ℤ) • a) | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | R (HAdd.hAdd (α := H) ((f : (a : G) → H) l : H) (n • b))
(HAdd.hAdd (α := H) ((f : (a : G) → H) (y - n • a) : H) (n • b)) | rw | [] | rw [← sub_add_cancel y (n • a), map_add_zsmul, map_add_zsmul] | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | l ∈ Icc l (l + a) | refine | [] | refine hR _ <| hf _ ?_ _ (Ioc_subset_Icc_self hny) hny.1 | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hy : R ((f : (a : G) → H) (l + n • a)) ((f : (a : G) → H) y)),
R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) y) | have | [] | have hy : R (f (l + n • a)) (f y) := by
rw [← sub_add_cancel y (n • a), map_add_zsmul, map_add_zsmul]
refine hR _ <| hf _ ?_ _ (Ioc_subset_Icc_self hny) hny.1; simpa | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | 1 ≤ n | hn₁ | [
"hn",
"hy"
] | rw [← Int.add_one_le_iff, zero_add] at hn | hypothesis | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hny : y - HSMul.hSMul (α := ℤ) 1 a ∈ Ioc l (l + a)) (hn : LE.le (α := ℤ) 1 1)
(hy : R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) y)),
R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) y) | inl | [
"n",
"hny",
"hn",
"hy"
] | rcases hn.eq_or_lt with rfl | hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (hn : 1 < n), R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) y) | inr | [] | rcases hn.eq_or_lt with rfl | hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | R ((f : (a : G) → H) (l + HSMul.hSMul (α := ℤ) 1 a)) ((f : (a : G) → H) (l + n • a)) | trans | [] | trans f (l + n • a) | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Mathlib.Algebra.AddConstMap.Basic | train | null | F : Type u_1
G : Type u_2
H : Type u_3
inst : FunLike F G H
a : G
b : H
inst_1 : AddCommGroup G
inst_2 : LinearOrder G
inst_3 : IsOrderedAddMonoid G
inst_4 : Archimedean G
inst_5 : AddGroup H
inst_6 : AddConstMapClass F G H a b
f : F
R : H → H → Prop
inst_7 : IsTrans H R
ha : 0 < a
l : G
hf : ∀ x ∈ Icc l (l + a), ∀ y ∈... | ∀ (k : ℤ),
R ((fun (x : ℤ) ↦ ((f : (a : G) → H) (l + x • a) : H)) k)
((fun (x : ℤ) ↦ ((f : (a : G) → H) (l + x • a) : H)) (k + 1)) | refine | [] | refine Int.rel_of_forall_rel_succ_of_lt R (f := (f <| l + · • a)) (fun k ↦ ?_) hn | goal | null | null | null | null | null | [
{
"content": "Consider the following Lean goal:\n```lean4\nF : Type u_1\nG : Type u_2\nH : Type u_3\ninst : FunLike F G H\na : G\nb : H\ninst_1 : AddCommGroup G\ninst_2 : LinearOrder G\ninst_3 : IsOrderedAddMonoid G\ninst_4 : Archimedean G\ninst_5 : AddGroup H\ninst_6 : AddConstMapClass F G H a b\nf : F\nR : H ... | [
{
"function": {
"description": "Submit a Lean 4 `have` statement.",
"name": "have",
"parameters": {
"additionalProperties": false,
"properties": {
"clear": {
"default": [],
"description": "Any hypotheses that are irrelevant for proving the goal... |
Canonical Drafter — extract data (raw)
Ground-truth drafter/premise data lifted from existing Mathlib proofs by
Training/ExtractData.lean. This is the raw pool (429303 draft rows,
664445 premise rows from: Mathlib). Every row is a real have / closed
subgoal taken from a checked proof, so there are no success/used flags to filter
on. Columns follow the uniform schema shared with the rollout dataset, so the two
pools concatenate cleanly.
config drafts
One row per have recovered from a Mathlib proof.
| column | type | meaning |
|---|---|---|
goal |
str | pretty-printed goal the have addresses |
type |
str | the have type |
name |
str | the have hypothesis name |
removals |
list[str] | hypotheses the have cleared |
tactic |
str | the ground-truth tactic that produced this step |
kind |
str | what the step is (e.g. goal, hypothesis) |
messages |
list | single user->assistant turn; the assistant turn is the have tool call |
tools |
list | tool schema offered to the model |
const, roundtrip, success, used, usedTactic, typeFromPp |
— | null for extract rows (rollout-only columns) |
Recommended drafter-SFT use: every row is a used, ground-truth draft — keep
all rows and project to {messages, tools} (loss on the final assistant turn
only). Optionally filter by kind.
config premises
One row per subgoal closed within an extracted proof, with the closing tactic and the library constants it used.
| column | type | meaning |
|---|---|---|
goal |
str | pretty-printed goal that was closed |
tactic |
str | the closing tactic / term |
premises |
list[str] | library constant names used by the closing proof |
const, roundtrip |
— | null for extract rows (rollout-only columns) |
Recommended premise-selection use: many rows have an empty premises list
(goal closed by rfl/simp with no library lemma); drop those if you only want
goals that needed premises.
Splitting
Both configs ship train and validation splits. The split is module-level
(all rows from one Mathlib file land in the same split, so no train/val leakage)
and is the canonical project split shared with the rollout pipeline — an explicit
list of modules bundled in this repo at mathlib_v1_splits/{train,val}_modules.txt,
not a hash. Every row also carries:
| column | type | meaning |
|---|---|---|
module |
str | source Mathlib module (file) the row came from |
split |
str | train or val, from data/splits/mathlib_v1/ |
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