Arith.shift_cancel: 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 150-152 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=150&end_line=152

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

# shift(k, a) < shift(k, b): a < b
def shift_cancel(+k: Nat, +a: Nat, +b: Nat, +h: {Nat.is_lt(C.shift(k, a), C.shift(k, b)) == True{} : Bool}) -> {Nat.is_lt(a, b) == True{} : Bool}:
  cancel_c(k, a, b, h, L.bool_cases(Nat.is_lt(a, b)))

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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=cancel_c
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=bool_cases
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift