feat: add Prod.Lex.right'

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Leonardo de Moura 2022-02-28 11:19:28 -08:00
parent 10657f5e81
commit 2ba3205f94

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@ -196,6 +196,9 @@ inductive Lex : α × β → α × β → Prop where
| left {a₁} (b₁) {a₂} (b₂) (h : ra a₁ a₂) : Lex (a₁, b₁) (a₂, b₂)
| right (a) {b₁ b₂} (h : rb b₁ b₂) : Lex (a, b₁) (a, b₂)
theorem Lex.right' {a₁ : α} {b₁ : β} (h₁ : a₁ = a₂) (h₂ : rb b₁ b₂) : Lex ra rb (a₁, b₁) (a₂, b₂) :=
h₁ ▸ Lex.right a₁ h₂
-- relational product based on ra and rb
inductive RProd : α × β → α × β → Prop where
| intro {a₁ b₁ a₂ b₂} (h₁ : ra a₁ a₂) (h₂ : rb b₁ b₂) : RProd (a₁, b₁) (a₂, b₂)