def sum_go

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/lists.bend:20

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S

20def sum_go(+xs: List<&2, Nat>, +acc: Nat) -> {M.sum_go(xs, acc) == Nat.add(acc, S.lsum(xs)) : Nat}:
21  match xs:
22    case Nil{}:
23      Equal.sym(Nat, Nat.add(acc, 0n), acc, A.add_zero(acc))
24    case Con{+x, +t}:
25      Equal.trans(Nat, M.sum_go(t, Nat.add(acc, x)), Nat.add(Nat.add(acc, x), S.lsum(t)), Nat.add(acc, Nat.add(x, S.lsum(t))), sum_go(t, Nat.add(acc, x)), A.add_assoc(acc, x, S.lsum(t)))