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Create add_right.kind

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Ferran Delgà 2021-12-04 18:59:50 +01:00 committed by GitHub
parent 6e8a09cc68
commit 1a2ef75255
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base/Nat/Order/add_right.kind Normal file
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Nat.Order.add.right(
a: Nat
b: Nat
c: Nat
Hyp: Equal<Bool>(Nat.lte(a, b), true)
): Equal<Bool>(Nat.lte(Nat.add(a, c), Nat.add(b, c)), true)
let lem = Nat.Order.add.left(a, b, c, Hyp)
let lem = Equal.rewrite<Nat>(
Nat.add(c, a), Nat.add(a, c), Nat.add.comm(c, a),
(x) Equal<Bool>(Nat.lte(x, Nat.add(c, b)), true), lem
)
let qed = Equal.rewrite<Nat>(
Nat.add(c, b), Nat.add(b, c), Nat.add.comm(c, b),
(x) Equal<Bool>(Nat.lte(Nat.add(a, c), x), true), lem
)
qed