PROOF.AP.wrap_lt: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1738-1741 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=1738&end_line=1741

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# s + k < 2s, for k < s
def AP.wrap_lt(+s: Nat, +k: Nat, hk: {Nat.is_lt(k, s) == True{} : Bool}) -> {Nat.is_lt(Nat.add(s, k), Nat.double(s)) == True{} : Bool}:
  %Equal.sym(Nat, Nat.double(s), Nat.add(s, s), UL.nat_double(s)) : {Nat.is_lt(Nat.add(s, k), _) == True{} : Bool}
  Equal.trans(Bool, Nat.is_lt(Nat.add(s, k), Nat.add(s, s)), Nat.is_lt(k, s), True{}, AP.lt_cancel(s, k, s), hk)

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lt_cancel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_double