Reduce.cancel_t: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend as Reduce
Lines 100-104 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&start_line=100&end_line=104

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

# lo + h t < d when lo + (1 + h) t < t + d
def cancel_t(+t: Nat, +lo: Nat, +h: Nat, +d: Nat, +hx: {Nat.is_lt(Nat.add(lo, Nat.mul(1n+h, t)), Nat.add(t, d)) == True{} : Bool}) -> {Nat.is_lt(Nat.add(lo, Nat.mul(h, t)), d) == True{} : Bool}:
  %Equal.sym(Bool, Nat.is_lt(Nat.add(lo, Nat.mul(h, t)), d), Nat.is_lt(Nat.add(t, Nat.add(lo, Nat.mul(h, t))), Nat.add(t, d)), Equal.sym(Bool, Nat.is_lt(Nat.add(t, Nat.add(lo, Nat.mul(h, t))), Nat.add(t, d)), Nat.is_lt(Nat.add(lo, Nat.mul(h, t)), d), WW.lt_cancel_l(t, Nat.add(lo, Nat.mul(h, t)), d))) : {_ == True{} : Bool}
  %Equal.sym(Nat, Nat.add(t, Nat.add(lo, Nat.mul(h, t))), Nat.add(lo, Nat.add(t, Nat.mul(h, t))), NA.add_swap(t, lo, Nat.mul(h, t))) : {Nat.is_lt(_, Nat.add(t, d)) == True{} : Bool}
  hx

Uses (8):
  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=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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_swap
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=lt_cancel_l