def jam1_eq

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/w64sh.bend:308

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64add.bend as WA

308def jam1_eq(+q: Nat) -> {Nat.add(Nat.mul(2n, Nat.div(q, 2n)), 1n) == 1n+Nat.double(C.half(q)) : Nat}:
309  +e = Equal.trans(Nat, Nat.mul(2n, Nat.div(q, 2n)), Nat.double(Nat.div(q, 2n)), Nat.double(C.half(q)), Equal.sym(Nat, Nat.double(Nat.div(q, 2n)), Nat.mul(2n, Nat.div(q, 2n)), NA.double_mul(Nat.div(q, 2n))), Equal.cong(Nat, Nat, z => Nat.double(z), Nat.div(q, 2n), C.half(q), Equal.sym(Nat, C.half(q), Nat.div(q, 2n), WA.half_div(q))))
310  Equal.trans(Nat, Nat.add(Nat.mul(2n, Nat.div(q, 2n)), 1n), 1n+Nat.mul(2n, Nat.div(q, 2n)), 1n+Nat.double(C.half(q)), WA.plus1(Nat.mul(2n, Nat.div(q, 2n))), Equal.cong(Nat, Nat, z => 1n+z, Nat.mul(2n, Nat.div(q, 2n)), Nat.double(C.half(q)), e))