url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_lt | [167, 1] | [177, 70] | apply Fin.ne_of_val_ne | case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
lt : ↑k < first
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j | case step.kj.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
lt : ↑k < first
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑j |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_lt | [167, 1] | [177, 70] | exact Nat.ne_of_lt (Nat.lt_of_lt_of_le lt (Nat.le_trans fi ij)) | case step.kj.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
lt : ↑k < first
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑j | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | induction p with
| refl => rfl
| step i j fi ij jl p ih =>
rw [ih]
rw [Vec.get_swap_neq _ i j k]
. apply Fin.ne_of_val_ne
exact Nat.ne_of_gt (Nat.lt_of_le_of_lt (Nat.le_trans ij jl) gt)
. apply Fin.ne_of_val_ne
exact Nat.ne_of_gt (Nat.lt_of_le_of_lt jl gt) | n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
p : permuted n first last arr1 arr2
k : Fin n
gt : last < ↑k
⊢ arr2[k] = arr1[k] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | rfl | case refl
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ : Vec α✝ n
⊢ arr✝[k] = arr✝[k] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | rw [ih] | case step
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ arr'✝[k] = arr✝[k] | case step
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ (arr✝.swap i j)[k] = arr✝[k] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | rw [Vec.get_swap_neq _ i j k] | case step
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ (arr✝.swap i j)[k] = arr✝[k] | case step.ki
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ i
case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | . apply Fin.ne_of_val_ne
exact Nat.ne_of_gt (Nat.lt_of_le_of_lt (Nat.le_trans ij jl) gt) | case step.ki
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ i
case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j | case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | . apply Fin.ne_of_val_ne
exact Nat.ne_of_gt (Nat.lt_of_le_of_lt jl gt) | case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | apply Fin.ne_of_val_ne | case step.ki
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ i | case step.ki.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑i |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | exact Nat.ne_of_gt (Nat.lt_of_le_of_lt (Nat.le_trans ij jl) gt) | case step.ki.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑i | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | apply Fin.ne_of_val_ne | case step.kj
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ k ≠ j | case step.kj.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑j |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Permutation.lean | permuted.get_gt | [179, 1] | [189, 52] | exact Nat.ne_of_gt (Nat.lt_of_le_of_lt jl gt) | case step.kj.h
n first last : Nat
α✝ : Type
arr1 arr2 : Vec α✝ n
k : Fin n
gt : last < ↑k
arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : arr'✝[k] = (arr✝.swap i j)[k]
⊢ ¬↑k = ↑j | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | induction jk with
| refl => exact Order.refl
| step h ih =>
apply Order.trans
. exact ih (Nat.lt_of_le_of_lt (Nat.le_succ ..) kn)
. apply assms | α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k : Nat
kn : k < n
jk : j ≤ k
⊢ arr[j] ≤ arr[k] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | exact Order.refl | case refl
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k : Nat
kn : j < n
⊢ arr[j] ≤ arr[j] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | apply Order.trans | case step
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[j] ≤ arr[m✝.succ] | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[j] ≤ ?step.y
case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ ?step.y ≤ arr[m✝.succ]
case step.y
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ α |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | . exact ih (Nat.lt_of_le_of_lt (Nat.le_succ ..) kn) | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[j] ≤ ?step.y
case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ ?step.y ≤ arr[m✝.succ]
case step.y
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ α | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[m✝] ≤ arr[m✝.succ] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | . apply assms | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[m✝] ≤ arr[m✝.succ] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | exact ih (Nat.lt_of_le_of_lt (Nat.le_succ ..) kn) | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[j] ≤ ?step.y | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/AdjacentSorted.lean | sorted_of_adjacentSorted | [4, 1] | [14, 18] | apply assms | case step.a
α : Type
inst✝ : Order α
n : Nat
arr : Vec α n
assms : ∀ (i : Nat) (isLt : i + 1 < n), arr[i] ≤ arr[i + 1]
j k m✝ : Nat
h : j.le m✝
ih : ∀ (kn : m✝ < n), arr[j] ≤ arr[m✝]
kn : m✝.succ < n
⊢ arr[m✝] ≤ arr[m✝.succ] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_eq | [28, 1] | [31, 26] | show (a.set i v).get i = v | α : Type
n : Nat
a : Vec α n
i : Fin n
v : α
⊢ (a.set i v)[i] = v | α : Type
n : Nat
a : Vec α n
i : Fin n
v : α
⊢ (a.set i v).get i = v |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_eq | [28, 1] | [31, 26] | simp [Vec.get, Vec.set] | α : Type
n : Nat
a : Vec α n
i : Fin n
v : α
⊢ (a.set i v).get i = v | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_ne | [33, 1] | [38, 56] | show (a.set i v).get j = a.get j | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ (a.set i v)[j] = a[j] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ (a.set i v).get j = a.get j |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_ne | [33, 1] | [38, 56] | simp [Vec.get, Vec.set] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ (a.set i v).get j = a.get j | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ (a.val.set ⟨↑i, ⋯⟩ v)[↑j] = a.val[↑j] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_ne | [33, 1] | [38, 56] | exact Array.get_set_ne (j := j.val) a.val ⟨i, by simp [a.property, i.isLt]⟩ v
(by simp [a.property, j.isLt]) (Fin.val_ne_of_ne h) | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ (a.val.set ⟨↑i, ⋯⟩ v)[↑j] = a.val[↑j] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_ne | [33, 1] | [38, 56] | simp [a.property, i.isLt] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ ↑i < a.val.size | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set_ne | [33, 1] | [38, 56] | simp [a.property, j.isLt] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i ≠ j
⊢ ↑j < a.val.size | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set | [40, 1] | [47, 35] | if h : i = j then
simp [h]
exact Vec.get_set_eq a j v
else
simp [h]
exact Vec.get_set_ne a i j v h | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
⊢ (a.set i v)[j] = if i = j then v else a[j] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set | [40, 1] | [47, 35] | simp [h] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i = j
⊢ (a.set i v)[j] = if i = j then v else a[j] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i = j
⊢ (a.set j v)[j] = v |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set | [40, 1] | [47, 35] | exact Vec.get_set_eq a j v | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : i = j
⊢ (a.set j v)[j] = v | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set | [40, 1] | [47, 35] | simp [h] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : ¬i = j
⊢ (a.set i v)[j] = if i = j then v else a[j] | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : ¬i = j
⊢ (a.set i v)[j] = a[j] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_set | [40, 1] | [47, 35] | exact Vec.get_set_ne a i j v h | α : Type
n : Nat
a : Vec α n
i j : Fin n
v : α
h : ¬i = j
⊢ (a.set i v)[j] = a[j] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.swap_def | [49, 1] | [54, 6] | simp [Vec.swap] | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ a.swap i j = (a.set i (a.get j)).set j (a.get i) | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ ⟨a.val.swap (Fin.cast ⋯ i) (Fin.cast ⋯ j), ⋯⟩ = (a.set i (a.get j)).set j (a.get i) |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.swap_def | [49, 1] | [54, 6] | apply Subtype.eq | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ ⟨a.val.swap (Fin.cast ⋯ i) (Fin.cast ⋯ j), ⋯⟩ = (a.set i (a.get j)).set j (a.get i) | case a
α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ ⟨a.val.swap (Fin.cast ⋯ i) (Fin.cast ⋯ j), ⋯⟩.val = ((a.set i (a.get j)).set j (a.get i)).val |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.swap_def | [49, 1] | [54, 6] | simp [Vec.get, Vec.set, Array.swap_def] | case a
α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ ⟨a.val.swap (Fin.cast ⋯ i) (Fin.cast ⋯ j), ⋯⟩.val = ((a.set i (a.get j)).set j (a.get i)).val | case a
α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (a.val.set (Fin.cast ⋯ i) a.val[↑j]).set ⟨↑j, ⋯⟩ a.val[↑i] = (a.val.set ⟨↑i, ⋯⟩ a.val[↑j]).set ⟨↑j, ⋯⟩ a.val[↑i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.swap_def | [49, 1] | [54, 6] | rfl | case a
α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (a.val.set (Fin.cast ⋯ i) a.val[↑j]).set ⟨↑j, ⋯⟩ a.val[↑i] = (a.val.set ⟨↑i, ⋯⟩ a.val[↑j]).set ⟨↑j, ⋯⟩ a.val[↑i] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_left | [56, 1] | [59, 39] | simp [Vec.swap_def, Vec.get_set, Vec.get_set_eq] | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (a.swap i j)[i] = a[j] | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (if j = i then a.get i else a.get j) = a[j] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_left | [56, 1] | [59, 39] | cases decEq j i <;> simp [*] <;> rfl | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (if j = i then a.get i else a.get j) = a[j] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_right | [61, 1] | [64, 6] | simp [Vec.swap_def, Vec.get_set_eq] | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ (a.swap i j)[j] = a[i] | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ a.get i = a[i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_right | [61, 1] | [64, 6] | rfl | α : Type
n : Nat
a : Vec α n
i j : Fin n
⊢ a.get i = a[i] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_neq | [66, 1] | [70, 68] | simp [Vec.swap_def] | α : Type
n : Nat
a : Vec α n
i j k : Fin n
ki : k ≠ i
kj : k ≠ j
⊢ (a.swap i j)[k] = a[k] | α : Type
n : Nat
a : Vec α n
i j k : Fin n
ki : k ≠ i
kj : k ≠ j
⊢ ((a.set i (a.get j)).set j (a.get i))[k] = a[k] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.get_swap_neq | [66, 1] | [70, 68] | rw [Vec.get_set_ne (h := kj.symm), Vec.get_set_ne (h := ki.symm)] | α : Type
n : Nat
a : Vec α n
i j k : Fin n
ki : k ≠ i
kj : k ≠ j
⊢ ((a.set i (a.get j)).set j (a.get i))[k] = a[k] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Vec.lean | Vec.getElem_eq_getElem | [72, 1] | [73, 59] | rfl | α : Type
n : Nat
a : Vec α n
i : Fin n
⊢ a[i] = a.val[↑i] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | induction arr, first, i, j, fi, ij using partitionImpl.induct with
| case1 arr first i j fi ij lt jl h prev ih =>
unfold partitionImpl
simp [*]
| @case2 arr first i j fi ij lt jl h swapped mid hm arr' eq ih =>
unfold partitionImpl
simp [*] at *
have ⟨p₂⟩ := ih
have p₁ : permuted n first j arr swapped := .step i j fi ij (Nat.le_refl _) .refl
exact ⟨p₁.trans $ p₂.cast_last (Nat.sub_le ..)⟩
| case3 arr first i j fi ij jn =>
simp [partitionImpl, *]
exact ⟨.refl⟩ | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
⊢ Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i j fi ij).snd) | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | unfold partitionImpl | case case1
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : arr[i] < arr[first]
prev : ↑i - 1 ≤ ↑j
ih : Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i.prev j jl prev).snd)
⊢ Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i j fi ij).snd) | case case1
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : arr[i] < arr[first]
prev : ↑i - 1 ≤ ↑j
ih : Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i.prev j jl prev).snd)
⊢ Nonempty
(permuted n (↑first) (↑j) arr
(if h : first < i then
let_fun this := ⋯;
if arr[i] < arr[first] then
let_fun this_1 := ⋯;
partitionImpl arr first i.prev j this this_1
else
let arr := (dbgTraceIfShared "swap1" arr).swap i j;
match partitionImpl arr first i.prev j.prev this ⋯ with
| (⟨mid, hm⟩, arr) => (⟨mid, ⋯⟩, arr)
else (⟨j, ⋯⟩, arr)).snd) |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | simp [*] | case case1
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : arr[i] < arr[first]
prev : ↑i - 1 ≤ ↑j
ih : Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i.prev j jl prev).snd)
⊢ Nonempty
(permuted n (↑first) (↑j) arr
(if h : first < i then
let_fun this := ⋯;
if arr[i] < arr[first] then
let_fun this_1 := ⋯;
partitionImpl arr first i.prev j this this_1
else
let arr := (dbgTraceIfShared "swap1" arr).swap i j;
match partitionImpl arr first i.prev j.prev this ⋯ with
| (⟨mid, hm⟩, arr) => (⟨mid, ⋯⟩, arr)
else (⟨j, ⋯⟩, arr)).snd) | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | unfold partitionImpl | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j.prev) swapped (partitionImpl swapped first i.prev j.prev jl ⋯).snd)
⊢ Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i j fi ij).snd) | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j.prev) swapped (partitionImpl swapped first i.prev j.prev jl ⋯).snd)
⊢ Nonempty
(permuted n (↑first) (↑j) arr
(if h : first < i then
let_fun this := ⋯;
if arr[i] < arr[first] then
let_fun this_1 := ⋯;
partitionImpl arr first i.prev j this this_1
else
let arr := (dbgTraceIfShared "swap1" arr).swap i j;
match partitionImpl arr first i.prev j.prev this ⋯ with
| (⟨mid, hm⟩, arr) => (⟨mid, ⋯⟩, arr)
else (⟨j, ⋯⟩, arr)).snd) |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | simp [*] at * | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j.prev) swapped (partitionImpl swapped first i.prev j.prev jl ⋯).snd)
⊢ Nonempty
(permuted n (↑first) (↑j) arr
(if h : first < i then
let_fun this := ⋯;
if arr[i] < arr[first] then
let_fun this_1 := ⋯;
partitionImpl arr first i.prev j this this_1
else
let arr := (dbgTraceIfShared "swap1" arr).swap i j;
match partitionImpl arr first i.prev j.prev this ⋯ with
| (⟨mid, hm⟩, arr) => (⟨mid, ⋯⟩, arr)
else (⟨j, ⋯⟩, arr)).snd) | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | have ⟨p₂⟩ := ih | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
p₂ : permuted n (↑first) (↑j - 1) swapped arr'
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | have p₁ : permuted n first j arr swapped := .step i j fi ij (Nat.le_refl _) .refl | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
p₂ : permuted n (↑first) (↑j - 1) swapped arr'
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
p₂ : permuted n (↑first) (↑j - 1) swapped arr'
p₁ : permuted n (↑first) (↑j) arr swapped
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | exact ⟨p₁.trans $ p₂.cast_last (Nat.sub_le ..)⟩ | case case2
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
lt : first < i
jl : ↑first ≤ ↑i - 1
h : ¬arr[i] < arr[first]
swapped : Vec α n := (dbgTraceIfShared "swap1" arr).swap i j
mid : Fin n
hm : first ≤ mid ∧ mid ≤ j.prev
arr' : Vec α n
eq : partitionImpl swapped first i.prev j.prev jl ⋯ = (⟨mid, hm⟩, arr')
ih : Nonempty (permuted n (↑first) (↑j - 1) swapped arr')
p₂ : permuted n (↑first) (↑j - 1) swapped arr'
p₁ : permuted n (↑first) (↑j) arr swapped
⊢ Nonempty (permuted n (↑first) (↑j) arr arr') | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | simp [partitionImpl, *] | case case3
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
jn : ¬first < i
⊢ Nonempty (permuted n (↑first) (↑j) arr (partitionImpl arr first i j fi ij).snd) | case case3
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
jn : ¬first < i
⊢ Nonempty (permuted n (↑first) (↑j) arr arr) |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | partitionImpl_permuted | [20, 1] | [36, 18] | exact ⟨.refl⟩ | case case3
α : Type
inst✝ : Ord α
n : Nat
first✝ i✝ j✝ : Fin n
arr : Vec α n
first i j : Fin n
fi : first ≤ i
ij : i ≤ j
jn : ¬first < i
⊢ Nonempty (permuted n (↑first) (↑j) arr arr) | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | let p := quickSort'_permuted arr | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
⊢ ∃ f, invertible f ∧ ∀ (i : Fin n), arr[i] = (quickSort' arr)[f i] | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∃ f, invertible f ∧ ∀ (i : Fin n), arr[i] = (quickSort' arr)[f i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | exists p.to_map | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∃ f, invertible f ∧ ∀ (i : Fin n), arr[i] = (quickSort' arr)[f i] | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ invertible p.to_map ∧ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | apply And.intro | α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ invertible p.to_map ∧ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] | case left
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ invertible p.to_map
case right
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | . exact permuted_map_invertible p | case left
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ invertible p.to_map
case right
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] | case right
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | . exact permuted_map_index p | case right
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | exact permuted_map_invertible p | case left
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ invertible p.to_map | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/QuickSortPermutation.lean | quickSort'_map_index_invertible | [74, 1] | [81, 31] | exact permuted_map_index p | case right
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
p : permuted n 0 (n - 1) arr (quickSort' arr) := quickSort'_permuted arr
⊢ ∀ (i : Fin n), arr[i] = (quickSort' arr)[p.to_map i] | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | show (compare x y).isLE ∨ (compare y x).isLE | α : Type
inst✝ : Order α
x y : α
⊢ x ≤ y ∨ y ≤ x | α : Type
inst✝ : Order α
x y : α
⊢ (compare x y).isLE = true ∨ (compare y x).isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | match cmp : compare x y with
| .lt | .eq => simp [Ordering.isLE, cmp]
| .gt =>
apply Or.inr
rw [←symm, cmp]
decide | α : Type
inst✝ : Order α
x y : α
⊢ (compare x y).isLE = true ∨ (compare y x).isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | simp [Ordering.isLE, cmp] | α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.eq
⊢ Ordering.eq.isLE = true ∨ (compare y x).isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | apply Or.inr | α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.isLE = true ∨ (compare y x).isLE = true | case h
α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.gt
⊢ (compare y x).isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | rw [←symm, cmp] | case h
α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.gt
⊢ (compare y x).isLE = true | case h
α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.swap.isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.total | [12, 1] | [19, 11] | decide | case h
α : Type
inst✝ : Order α
x y : α
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.swap.isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | match cmp : compare x x with
| .eq => rfl
| .lt =>
have h₁ : (compare x x).swap = .gt := by rw [cmp]; decide
have h₂ : (compare x x).swap = .lt := by rw [symm]; assumption
rw [h₂] at h₁
contradiction
| .gt =>
have h₁ : (compare x x).swap = .lt := by rw [cmp]; decide
have h₂ : (compare x x).swap = .gt := by rw [symm]; assumption
rw [h₂] at h₁
contradiction | α : Type
inst✝ : Order α
x : α
⊢ compare x x = Ordering.eq | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rfl | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.eq
⊢ Ordering.eq = Ordering.eq | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | have h₁ : (compare x x).swap = .gt := by rw [cmp]; decide | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
⊢ Ordering.lt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
⊢ Ordering.lt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | have h₂ : (compare x x).swap = .lt := by rw [symm]; assumption | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
⊢ Ordering.lt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
h₂ : (compare x x).swap = Ordering.lt
⊢ Ordering.lt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [h₂] at h₁ | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
h₂ : (compare x x).swap = Ordering.lt
⊢ Ordering.lt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : Ordering.lt = Ordering.gt
h₂ : (compare x x).swap = Ordering.lt
⊢ Ordering.lt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | contradiction | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : Ordering.lt = Ordering.gt
h₂ : (compare x x).swap = Ordering.lt
⊢ Ordering.lt = Ordering.eq | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [cmp] | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
⊢ (compare x x).swap = Ordering.gt | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
⊢ Ordering.lt.swap = Ordering.gt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | decide | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
⊢ Ordering.lt.swap = Ordering.gt | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [symm] | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
⊢ (compare x x).swap = Ordering.lt | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
⊢ compare x x = Ordering.lt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | assumption | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.lt
h₁ : (compare x x).swap = Ordering.gt
⊢ compare x x = Ordering.lt | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | have h₁ : (compare x x).swap = .lt := by rw [cmp]; decide | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
⊢ Ordering.gt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
⊢ Ordering.gt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | have h₂ : (compare x x).swap = .gt := by rw [symm]; assumption | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
⊢ Ordering.gt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
h₂ : (compare x x).swap = Ordering.gt
⊢ Ordering.gt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [h₂] at h₁ | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
h₂ : (compare x x).swap = Ordering.gt
⊢ Ordering.gt = Ordering.eq | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : Ordering.gt = Ordering.lt
h₂ : (compare x x).swap = Ordering.gt
⊢ Ordering.gt = Ordering.eq |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | contradiction | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : Ordering.gt = Ordering.lt
h₂ : (compare x x).swap = Ordering.gt
⊢ Ordering.gt = Ordering.eq | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [cmp] | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
⊢ (compare x x).swap = Ordering.lt | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
⊢ Ordering.gt.swap = Ordering.lt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | decide | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
⊢ Ordering.gt.swap = Ordering.lt | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | rw [symm] | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
⊢ (compare x x).swap = Ordering.gt | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
⊢ compare x x = Ordering.gt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.cmp_eq_of_eq | [21, 1] | [33, 18] | assumption | α : Type
inst✝ : Order α
x : α
cmp : compare x x = Ordering.gt
h₁ : (compare x x).swap = Ordering.lt
⊢ compare x x = Ordering.gt | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.refl | [35, 1] | [38, 9] | show (compare x x).isLE | α : Type
inst✝ : Order α
x : α
⊢ x ≤ x | α : Type
inst✝ : Order α
x : α
⊢ (compare x x).isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.refl | [35, 1] | [38, 9] | simp [cmp_eq_of_eq] | α : Type
inst✝ : Order α
x : α
⊢ (compare x x).isLE = true | α : Type
inst✝ : Order α
x : α
⊢ Ordering.eq.isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.refl | [35, 1] | [38, 9] | decide | α : Type
inst✝ : Order α
x : α
⊢ Ordering.eq.isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.irrefl | [40, 1] | [41, 31] | simp [ltOfOrd, cmp_eq_of_eq] | α : Type
inst✝ : Order α
x : α
⊢ ¬x < x | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | show (compare x y).isLE | α : Type
inst✝ : Order α
x y : α
h : ¬y < x
⊢ x ≤ y | α : Type
inst✝ : Order α
x y : α
h : ¬y < x
⊢ (compare x y).isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | match cmp : compare x y with
| .lt | .eq => decide
| .gt =>
simp [ltOfOrd] at h
have : compare y x = .lt := by rw [←symm, cmp]; decide
rw [this] at h
contradiction | α : Type
inst✝ : Order α
x y : α
h : ¬y < x
⊢ (compare x y).isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | decide | α : Type
inst✝ : Order α
x y : α
h : ¬y < x
cmp : compare x y = Ordering.eq
⊢ Ordering.eq.isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | simp [ltOfOrd] at h | α : Type
inst✝ : Order α
x y : α
h : ¬y < x
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.isLE = true | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | have : compare y x = .lt := by rw [←symm, cmp]; decide | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.isLE = true | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
this : compare y x = Ordering.lt
⊢ Ordering.gt.isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | rw [this] at h | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
this : compare y x = Ordering.lt
⊢ Ordering.gt.isLE = true | α : Type
inst✝ : Order α
x y : α
h : ¬Ordering.lt = Ordering.lt
cmp : compare x y = Ordering.gt
this : compare y x = Ordering.lt
⊢ Ordering.gt.isLE = true |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | contradiction | α : Type
inst✝ : Order α
x y : α
h : ¬Ordering.lt = Ordering.lt
cmp : compare x y = Ordering.gt
this : compare y x = Ordering.lt
⊢ Ordering.gt.isLE = true | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | rw [←symm, cmp] | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
⊢ compare y x = Ordering.lt | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.swap = Ordering.lt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.le_of_not_lt | [43, 1] | [51, 18] | decide | α : Type
inst✝ : Order α
x y : α
h : ¬compare y x = Ordering.lt
cmp : compare x y = Ordering.gt
⊢ Ordering.gt.swap = Ordering.lt | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.not_lt_of_le | [53, 1] | [61, 18] | match cmp : compare x y with
| .lt | .eq =>
simp [ltOfOrd]
rw [←symm, cmp]
decide
| .gt =>
simp [leOfOrd, cmp] at h
contradiction | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
⊢ ¬y < x | no goals |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.not_lt_of_le | [53, 1] | [61, 18] | simp [ltOfOrd] | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
cmp : compare x y = Ordering.eq
⊢ ¬y < x | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
cmp : compare x y = Ordering.eq
⊢ ¬compare y x = Ordering.lt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.not_lt_of_le | [53, 1] | [61, 18] | rw [←symm, cmp] | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
cmp : compare x y = Ordering.eq
⊢ ¬compare y x = Ordering.lt | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
cmp : compare x y = Ordering.eq
⊢ ¬Ordering.eq.swap = Ordering.lt |
https://github.com/pandaman64/QuickSortInLean.git | ab0aaee0aed280959328844f9a6cd13bf00c5935 | QuickSortInLean/Order.lean | Order.not_lt_of_le | [53, 1] | [61, 18] | decide | α : Type
inst✝ : Order α
x y : α
h : x ≤ y
cmp : compare x y = Ordering.eq
⊢ ¬Ordering.eq.swap = Ordering.lt | no goals |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.