Impl.fS: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/impl.bend as Impl
Lines 41-43 of bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/impl.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/impl.bend&start_line=41&end_line=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/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA

# a sum mod 2^64
def fS(+a: WU.U64, +b: WU.U64) -> {C.low(64n, SW.value(X.add(a, b))) == C.low(64n, Nat.add(SW.value(a), SW.value(b))) : Nat}:
  eqm_of(SW.value(X.add(a, b)), Nat.add(SW.value(a), SW.value(b)), WA.add_value(a, b))

Uses (8):
  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=bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/impl.bend&name=eqm_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=add_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=low
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  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=add