def P2

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64dm.bend:52

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
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/math/typed/width.bend as WW

52def P2(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(2n, C.shift(32n, one)) == True{} : Bool}:
53  +h = L.subst(Nat, z => {Nat.is_le(z, C.shift(31n, one)) == True{} : Bool}, one, 1n, h1, WW.shift_ge(31n, one))
54  N.double_le(1n, C.shift(31n, one), h)