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def dvd_trans

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/lists.bend:53

import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend as Lists
import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

53# (a == k1 b and b == k2 c) gives a == (k1 k2) c
54def dvd_trans(+a: Nat, +b: Nat, +c: Nat, +k1: Nat, +k2: Nat, +e1: {a == Nat.mul(k1, b) : Nat}, +e2: {b == Nat.mul(k2, c) : Nat}) -> {a == Nat.mul(Nat.mul(k1, k2), c) : Nat}:
55  Equal.trans(Nat, a, Nat.mul(k1, b), Nat.mul(Nat.mul(k1, k2), c), e1, Equal.trans(Nat, Nat.mul(k1, b), Nat.mul(k1, Nat.mul(k2, c)), Nat.mul(Nat.mul(k1, k2), c), Equal.cong(Nat, Nat, z => Nat.mul(k1, z), b, Nat.mul(k2, c), e2), Equal.sym(Nat, Nat.mul(Nat.mul(k1, k2), c), Nat.mul(k1, Nat.mul(k2, c)), A.mul_assoc(k1, k2, c))))

Uses (6)

Used by (4)