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Author SHA1 Message Date
Kim Morrison
7a3333bf30 chore: defs that should be theorems 2024-07-02 12:50:32 +10:00

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@@ -288,7 +288,7 @@ instance [ha : WellFoundedRelation α] [hb : WellFoundedRelation β] : WellFound
lex ha hb
-- relational product is a Subrelation of the Lex
def RProdSubLex (a : α × β) (b : α × β) (h : RProd ra rb a b) : Prod.Lex ra rb a b := by
theorem RProdSubLex (a : α × β) (b : α × β) (h : RProd ra rb a b) : Prod.Lex ra rb a b := by
cases h with
| intro h₁ h₂ => exact Prod.Lex.left _ _ h₁
@@ -320,7 +320,7 @@ section
variable {α : Sort u} {β : α Sort v}
variable {r : α α Prop} {s : (a : α), β a β a Prop}
def lexAccessible {a} (aca : Acc r a) (acb : (a : α) WellFounded (s a)) (b : β a) : Acc (Lex r s) a, b := by
theorem lexAccessible {a} (aca : Acc r a) (acb : (a : α) WellFounded (s a)) (b : β a) : Acc (Lex r s) a, b := by
induction aca with
| intro xa _ iha =>
induction (WellFounded.apply (acb xa) b) with