def bound32

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/words32.bend:98

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

98def bound32(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +d: Nat, +hd: {Nat.is_lt(1n+d, 32n) == True{} : Bool}, +hx: {Nat.is_lt(x, SC.pow2(d)) == True{} : Bool}) -> {Nat.is_lt(1n+x, WD.sc(32n, one)) == True{} : Bool}:
99  N.le_lt_trans(1n+x, SC.pow2(d), WD.sc(32n, one), N.lt_succ_le_succ(x, SC.pow2(d), hx), N.lt_le_trans(SC.pow2(d), SC.pow2(1n+d), WD.sc(32n, one), N.pow2_lt_succ(d), pow_le32(one, h1, 1n+d, hd)))