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1 changed files with 3 additions and 3 deletions
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@ -153,8 +153,8 @@ section
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-- Lexicographical order based on ra and rb
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inductive lex : α × β → α × β → Prop
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| left : ∀ {a₁ b₁} a₂ b₂, ra a₁ a₂ → lex (a₁, b₁) (a₂, b₂)
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| right : ∀ a {b₁ b₂}, rb b₁ b₂ → lex (a, b₁) (a, b₂)
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| left : ∀ {a₁} b₁ {a₂} b₂, ra a₁ a₂ → lex (a₁, b₁) (a₂, b₂)
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| right : ∀ a {b₁ b₂}, rb b₁ b₂ → lex (a, b₁) (a, b₂)
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-- relational product based on ra and rb
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inductive rprod : α × β → α × β → Prop
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@ -183,7 +183,7 @@ section
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-- relational product is a subrelation of the lex
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def rprod_sub_lex : ∀ a b, rprod ra rb a b → lex ra rb a b :=
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λ a b h, prod.rprod.rec_on h (λ a₁ b₁ a₂ b₂ h₁ h₂, lex.left rb a₂ b₂ h₁)
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λ a b h, prod.rprod.rec_on h (λ a₁ b₁ a₂ b₂ h₁ h₂, lex.left rb b₁ b₂ h₁)
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-- The relational product of well founded relations is well-founded
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def rprod_wf (ha : well_founded ra) (hb : well_founded rb) : well_founded (rprod ra rb) :=
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