Idris2/tests/idris2/with/with010/NestedWith.idr

module NestedWith

%default total

interface DecEq a where
  decEq : (x, y : a) -> Dec (x === y)

(DecEq a, DecEq b) => DecEq (a, b) where
  decEq (x, y) (a, b) with (decEq x a) | (decEq y b)
    _ | Yes eqL | Yes eqR = Yes (cong2 (,) eqL eqR)
    _ | No neqL | _ = No $ \prf => neqL $ cong fst prf
    _ | _ | No neqR = No $ \prf => neqR $ cong snd prf
[ new ] multi-with elaborated as nested withs (#2403) 2022-04-07 11:30:23 +03:00			`module NestedWith`

			`%default total`

			`interface DecEq a where`
			`decEq : (x, y : a) -> Dec (x === y)`

			`(DecEq a, DecEq b) => DecEq (a, b) where`
			`decEq (x, y) (a, b) with (decEq x a) \| (decEq y b)`
			`_ \| Yes eqL \| Yes eqR = Yes (cong2 (,) eqL eqR)`
Generalize Prelude proof helpers 2023-06-11 16:23:16 +03:00			`_ \| No neqL \| _ = No $ \prf => neqL $ cong fst prf`
			`_ \| _ \| No neqR = No $ \prf => neqR $ cong snd prf`