def gall

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:194

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

194def 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}:
195  match xs:
196    case Nil{}:
197      {==}
198    case Con{+x, +t}:
199      +g = G.gcd(~WU.U64, ~I.u64_op, ~I.u64_is, acc, x)
200      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)))