3770b3dcb8
This PR fixed typos: ``` pip install codespell --upgrade codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames --regex '[A-Z][a-z]*' codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames --regex "\b[a-z']*" ```
44 lines
860 B
Text
44 lines
860 B
Text
module
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inductive T (a:Type) where
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| constructor1: T a
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| constructor2: T a
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instance : LE (T a) where
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le := sorry
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axiom L: Type
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axiom L.pred (l1: L) (t: T α): Prop
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axiom L.pred_le (l1: L) (t1 t2: T α):
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t1 ≤ t2 → l1.pred t1 → l1.pred t2
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grind_pattern L.pred_le => t1 ≤ t2, l1.pred t1
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abbrev T' := T Unit
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axiom l (t: T'): L
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-- l keeps the same value when t gets bigger
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axiom l_le (t1 t2: T'):
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t1 ≤ t2 → l t1 = l t2
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grind_pattern l_le => t1 ≤ t2, l t1
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-- construction using l and L.pred
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abbrev pred (t: T'): Prop :=
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(l t).pred t
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example: pred t1 → t1 ≤ t2 → pred t2 := by
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grind
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example: t1 ≤ t2 → pred t1 → pred t2 := by
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grind
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def is_mono (p: T' → Prop): Prop :=
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∀ t1 t2,
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p t1 → t1 ≤ t2 → p t2
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example: is_mono pred := by
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grind [is_mono]
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example: is_mono pred := by
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unfold is_mono
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grind
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