def cancel_t

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/reduce.bend:100

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

100# lo + h t < d when lo + (1 + h) t < t + d
101def 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}:
102  %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}
103  %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}
104  hx