def lt_of

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:84

import Base
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/u64laws.bend as LW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

84def lt_of(+a: WU.U64, +b: WU.U64, +c: Bool, +hc: {I.u64_is(NM.Lt{a, b}) == c : Bool}) -> {Nat.is_lt(v(a), v(b)) == c : Bool}:
85  Equal.trans(Bool, Nat.is_lt(v(a), v(b)), I.u64_is(NM.Lt{a, b}), c, Equal.sym(Bool, I.u64_is(NM.Lt{a, b}), Nat.is_lt(v(a), v(b)), LW.tests_lt(a, b)), hc)