def le16

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64sqrt.bend:251

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

251def le16(+one: Nat, +h1: {one == 1n : Nat}, +r: U32, +m: U32, +pm: {m == U32{WD.mask(32n, 16n)} : U32}, +h: {Nat.is_lt(v(r), WD.sc(16n, one)) == True{} : Bool}) -> {Nat.is_le(v(r), v(m)) == True{} : Bool}:
252  N.lt_succ_le(v(r), v(m), L.subst(Nat, z => {Nat.is_lt(v(r), z) == True{} : Bool}, WD.sc(16n, one), 1n+v(m), Equal.sym(Nat, 1n+v(m), WD.sc(16n, one), m16(one, h1, m, pm)), h))