def mcons
bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64add.bend:339
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as W64add
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/typed/w64mul.bend as W64M
339def mcons(+x: U32, +y: U32) -> {Nat.add(v(U32.mul(x, y)), C.shift(32n, W64M.mex(x, y))) == Nat.mul(v(x), v(y)) : Nat}:
340 Equal.trans(Nat, Nat.add(v(U32.mul(x, y)), C.shift(32n, W64M.mex(x, y))), Nat.add(v(U32.mul(x, y)), WD.sc(32n, W64M.mex(x, y))), Nat.mul(v(x), v(y)), Equal.cong(Nat, Nat, z => Nat.add(v(U32.mul(x, y)), z), C.shift(32n, W64M.mex(x, y)), WD.sc(32n, W64M.mex(x, y)), W64M.shift_sc(32n, W64M.mex(x, y))), W64M.mul_cons(x, y))