def lt_one

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

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

251def lt_one(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +h: {C.fits(k, x) == True{} : Bool}) -> {Nat.is_lt(x, C.shift(k, one)) == True{} : Bool}:
252  +h2 = L.subst(Nat, z => {Nat.is_lt(x, z) == True{} : Bool}, C.pow2(k), C.shift(k, 1n), Equal.sym(Nat, C.shift(k, 1n), C.pow2(k), shift_one(k)), lt_of_fits(k, x, h))
253  L.subst(Nat, z => {Nat.is_lt(x, C.shift(k, z)) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), h2)