U64int.gall: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend as U64int
Lines 194-200 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&start_line=194&end_line=200

import Base
import bend-collections-laws-math@1.0.0.0/src/math/generic.bend as G
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/src/math/instances.bend as I
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

def gall(+xs: List<&2, WU.U64>, +acc: WU.U64) -> {v(G.gcd_all_go(~WU.U64, ~I.u64_op, ~I.u64_is, xs, acc)) == M.gcd_all_go(vals(xs), v(acc)) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{+x, +t}:
      +g = G.gcd(~WU.U64, ~I.u64_op, ~I.u64_is, acc, x)
      Equal.trans(Nat, v(G.gcd_all_go(~WU.U64, ~I.u64_op, ~I.u64_is, t, g)), M.gcd_all_go(vals(t), v(g)), M.gcd_all_go(vals(t), M.gcd(v(acc), v(x))), gall(t, g), Equal.cong(Nat, Nat, z => M.gcd_all_go(vals(t), z), v(g), M.gcd(v(acc), v(x)), gcd_val(acc, x)))

Uses (14):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&name=gcd_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&name=vals
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/generic.bend&name=gcd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/generic.bend&name=gcd_all_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/instances.bend&name=u64_is
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/instances.bend&name=u64_op
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=gcd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=gcd_all_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64