def mval

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64sqrt.bend:41

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32.bend as U32P

41def mval(+n: Nat, +k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +hk: {Nat.is_le(k, n) == True{} : Bool}) -> {1n+WD.uw(n, WD.mask(n, k)) == WD.sc(k, one) : Nat}:
42  match n k:
43    case 0n 0n:
44      Equal.sym(Nat, one, 1n, h1)
45    case 0n 1n+j:
46      Empty.absurd({1n+WD.uw(0n, WD.mask(0n, 1n+j)) == WD.sc(1n+j, one) : Nat}, U32P.true_ne_false(Equal.sym(Bool, False{}, True{}, hk)))
47    case 1n+ +p 0n:
48      %Equal.sym(Nat, WD.uw(p, WD.mask(p, 0n)), 0n, mz(p)) : {1n+Nat.add(0n, Nat.double(_)) == WD.sc(0n, one) : Nat}
49      Equal.sym(Nat, one, 1n, h1)
50    case 1n+ +p 1n+ +j:
51      Equal.cong(Nat, Nat, t => Nat.double(t), 1n+WD.uw(p, WD.mask(p, j)), WD.sc(j, one), mval(p, j, one, h1, hk))