def lt_of

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u32int.bend:82

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/u32laws.bend as LW

82def lt_of(+a: U32, +b: U32, +c: Bool, +hc: {I.u32_is(NM.Lt{a, b}) == c : Bool}) -> {Nat.is_lt(v(a), v(b)) == c : Bool}:
83  Equal.trans(Bool, Nat.is_lt(v(a), v(b)), I.u32_is(NM.Lt{a, b}), c, Equal.sym(Bool, I.u32_is(NM.Lt{a, b}), Nat.is_lt(v(a), v(b)), LW.tests_lt(a, b)), hc)