W64m128.val0: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64m128.bend as W64m128
Lines 78-79 of bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64m128.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64m128.bend&start_line=78&end_line=79

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/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

def val0(+x: U32) -> {SW.value(WU.U64{x, 0}) == v(x) : Nat}:
  Equal.trans(Nat, Nat.add(v(x), C.shift(32n, 0n)), Nat.add(v(x), 0n), v(x), Equal.cong(Nat, Nat, z => Nat.add(v(x), z), C.shift(32n, 0n), 0n, WW.shift_zero(32n)), N.add_zero(v(x)))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64m128.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=U64