def max_val_c

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:107

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/num.bend as NM
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/u32.bend as U32P
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

107def max_val_c(+x: WU.U64, +lo: WU.U64, +c: Bool, +hc: {I.u64_is(NM.Lt{x, lo}) == c : Bool}) -> {v(G.pick(WU.U64, c, lo, x)) == Nat.max(v(x), v(lo)) : Nat}:
108  match c:
109    case True{}:
110      Equal.sym(Nat, Nat.max(v(x), v(lo)), v(lo), U32P.max_of_lt(v(x), v(lo), lt_of(x, lo, True{}, hc)))
111    case False{}:
112      Equal.sym(Nat, Nat.max(v(x), v(lo)), v(x), U32P.max_of_ge(v(x), v(lo), lt_of(x, lo, False{}, hc)))