def acons

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64add.bend:43

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend as P64
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend as W64M

43# x + y == (x + y mod 2^32) + 2^32 carry
44def acons(+x: U32, +y: U32) -> {Nat.add(v(U32.add(x, y)), C.shift(32n, bv(P64.carry32(x, y)))) == Nat.add(v(x), v(y)) : Nat}:
45  +c = bv(P64.carry32(x, y))
46  Equal.trans(Nat, Nat.add(v(U32.add(x, y)), C.shift(32n, c)), Nat.add(v(U32.add(x, y)), WD.sc(32n, c)), Nat.add(v(x), v(y)), Equal.cong(Nat, Nat, t => Nat.add(v(U32.add(x, y)), t), C.shift(32n, c), WD.sc(32n, c), W64M.shift_sc(32n, c)), P64.add_cons(x, y))