def lall

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:288

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/generic.bend as SG
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/num.bend as NM
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/proofs/math/typed/u64laws.bend as LW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

288# the fold on an accumulator r == checked(n) (c == fits(32, n))
289def lall(+xs: List<&2, WU.U64>, +r: Result<&2, &2, NM.NumError, WU.U64>, +n: Nat, +c: Bool, +hr: {r == SG.checked_pick(~WU.U64, ~SG.u64_of, n, c) : Result<&2, &2, NM.NumError, WU.U64>}, +hc: {C.fits(64n, n) == c : Bool}) -> {G.lcm_all_go(~WU.U64, ~I.u64_op, ~I.u64_is, xs, r) == SG.prefix_fin(~WU.U64, ~SG.u64_of, SG.lcm_go(64n, vals(xs), n, c)) : Result<&2, &2, NM.NumError, WU.U64>}:
290  match xs c:
291    case Nil{} _:
292      hr
293    case Con{x, t} False{}:
294      %Equal.sym(Result<&2, &2, NM.NumError, WU.U64>, r, Fail{NM.Overflow{}}, hr) : {G.lcm_all_go(~WU.U64, ~I.u64_op, ~I.u64_is, Con{x, t}, _) == Fail{NM.Overflow{}} : Result<&2, &2, NM.NumError, WU.U64>}
295      {==}
296    case Con{+x, +t} True{}:
297      %Equal.sym(Result<&2, &2, NM.NumError, WU.U64>, r, Done{of(n)}, hr) : {G.lcm_all_go(~WU.U64, ~I.u64_op, ~I.u64_is, Con{x, t}, _) == SG.prefix_fin(~WU.U64, ~SG.u64_of, SG.lcm_go(64n, vals(t), M.lcm(n, v(x)), C.fits(64n, M.lcm(n, v(x))))) : Result<&2, &2, NM.NumError, WU.U64>}
298      +en = LW.vo(n, hc)
299      +el = Equal.trans(Result<&2, &2, NM.NumError, WU.U64>, G.lcm(~WU.U64, ~I.u64_op, ~I.u64_is, of(n), x), SG.checked(~WU.U64, ~SG.u64_of, 64n, M.lcm(v(of(n)), v(x))), SG.checked(~WU.U64, ~SG.u64_of, 64n, M.lcm(n, v(x))), lcm_checked(of(n), x), Equal.cong(Nat, Result<&2, &2, NM.NumError, WU.U64>, z => SG.checked(~WU.U64, ~SG.u64_of, 64n, M.lcm(z, v(x))), v(of(n)), n, en))
300      lall(t, G.lcm(~WU.U64, ~I.u64_op, ~I.u64_is, of(n), x), M.lcm(n, v(x)), C.fits(64n, M.lcm(n, v(x))), el, {==})