Nat.pow2_strict: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 460-465 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=460&end_line=465

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def pow2_strict(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_lt(SC.pow2(a), SC.pow2(b)) == True{} : Bool}:
  match b:
    case 0n:
      Empty.absurd({Nat.is_lt(SC.pow2(a), 1n) == True{} : Bool}, lt_zero_absurd(a, e))
    case 1n+q:
      lt_le_trans(SC.pow2(a), SC.pow2(1n+a), SC.pow2(1n+q), pow2_lt_succ(a), pow2_mono(1n+a, 1n+q, lt_succ_le_succ(a, 1n+q, e)))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=pow2_lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=pow2_mono
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2