Arith.one_le_shift: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as Arith
Lines 114-116 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&start_line=114&end_line=116

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
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

# 1 <= 2^k
def one_le_shift(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(1n, C.shift(k, one)) == True{} : Bool}:
  L.subst(Nat, z => {Nat.is_le(z, C.shift(k, one)) == True{} : Bool}, one, 1n, h1, WW.shift_ge(k, one))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_ge
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift