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Create add_combine

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Ferran Delgà 2021-12-04 18:56:44 +01:00 committed by GitHub
parent 77080b3a82
commit 2028e137c7
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base/Nat/Order/add_combine Normal file
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Nat.Order.add.combine(
a: Nat
b: Nat
c: Nat
d: Nat
Hyp0: Equal<Bool>(Nat.lte(a, b), true)
Hyp1: Equal<Bool>(Nat.lte(c, d), true)
): Equal<Bool>(Nat.lte(Nat.add(a, c), Nat.add(b, d)), true)
let left_lem = Nat.Order.add.right(a, b, c, Hyp0)
let right_lem = Nat.Order.add.left(c, d, b, Hyp1)
let qed = Nat.Order.Transitivity(Nat.add(a, c), Nat.add(b, c), Nat.add(b,d), left_lem, right_lem)
qed