W64mul.impl: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend as W64mul
Lines 269-272 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&start_line=269&end_line=272

import Base
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/shrn.bend as SR

def impl(+a: U32, +b: U32) -> {X.mul32(a, b) == mul32g(a, b, 65536, 65535) : WU.U64}:
  %Equal.sym(U32, U32.shrn(a, 16n), U32.div(a, 65536), SR.shr16(a)) : {X.mul32_h(U32.and(a, 65535), _, U32.and(b, 65535), U32.shrn(b, 16n)) == mul32g(a, b, 65536, 65535) : WU.U64}
  %Equal.sym(U32, U32.shrn(b, 16n), U32.div(b, 65536), SR.shr16(b)) : {X.mul32_h(U32.and(a, 65535), U32.div(a, 65536), U32.and(b, 65535), _) == mul32g(a, b, 65536, 65535) : WU.U64}
  h_eq(U32.and(a, 65535), U32.div(a, 65536), U32.and(b, 65535), U32.div(b, 65536))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/shrn.bend&name=shr16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&name=h_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend&name=mul32g
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=mul32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=mul32_h