[Merged by Bors] - fix: correct String.instLinearOrderString#3339
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[Merged by Bors] - fix: correct String.instLinearOrderString#3339
String.instLinearOrderString#3339Conversation
Use the optimized `compare` function and provide a manual `compare_eq_compareOfLessAndEq` field.
Use the tactic combinator `<;>` to golf the proof.
Mathlib/Data/String/Basic.lean
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| theorem List.lt_iff_lex_char_lt (l l' : List Char) : List.lt l l' ↔ List.Lex Char.lt l l' := by | ||
| constructor <;> | ||
| intro h | ||
| · induction h with | ||
| | nil b bs => exact Lex.nil | ||
| | @head a as b bs hab => apply Lex.rel; assumption | ||
| | @tail a as b bs hab hba _ ih => | ||
| have heq : a = b := _root_.le_antisymm (le_of_not_lt hba) (le_of_not_lt hab) | ||
| subst b; apply Lex.cons; assumption | ||
| · induction h with | ||
| | @nil a as => apply List.lt.nil | ||
| | @cons a as bs _ ih => apply List.lt.tail <;> simp [ih] | ||
| | @rel a as b bs h => apply List.lt.head; assumption |
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Note that there's nothing specific about Char in this proof; the following works:
theorem List.lt_eq_lt [LinearOrder α] (l₁ l₂ : List α) : List.lt l₁ l₂ ↔ l₁ < l₂ := by
dsimp only [List.LT', List.lt]
constructor
· intro h
induction h with
| nil b bs => exact Lex.nil
| @head a as b bs hab => apply Lex.rel; assumption
| @tail a as b bs hab hba _ ih =>
have heq : a = b := _root_.le_antisymm (le_of_not_lt hba) (le_of_not_lt hab)
subst b; apply Lex.cons; assumption
· intro h
induction h with
| @nil a as => apply List.lt.nil
| @cons a as bs _ ih => apply List.lt.tail <;> simp [ih]
| @rel a as b bs h => apply List.lt.head; assumption
theorem List.lt_iff_lex_char_lt (l l' : List Char) : List.lt l l' ↔ List.Lex Char.lt l l' :=
List.lt_eq_lt l l'(Why do we override the LT instance on List anyway?)
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Some of this might be a mess made by porting stuff that std4 already had a competing implementation of.
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Author
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Note that there's nothing specific about
Charin this proof;
I changed the theorem List.lt_iff_lex_char_lt to List.lt_iff_lex_lt.
* Change the theorem `List.lt_iff_lex_char_lt` to `List.lt_iff_lex_lt`. * Lint code.
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bors merge |
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Use the optimized `compare` function and provide a manual `compare_eq_compareOfLessAndEq` field.
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Pull request successfully merged into master. Build succeeded: |
String.instLinearOrderStringString.instLinearOrderString
MonadMaverick
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Apr 9, 2023
Use the optimized `compare` function and provide a manual `compare_eq_compareOfLessAndEq` field.
MonadMaverick
pushed a commit
that referenced
this pull request
Apr 9, 2023
Use the optimized `compare` function and provide a manual `compare_eq_compareOfLessAndEq` field.
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Use the optimized
comparefunction and provide a manualcompare_eq_compareOfLessAndEqfield.