def rpp_cong

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64mont.bend:180

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

180def rpp_cong(+one: Nat, +h1: {one == 1n : Nat}, +bp: Nat, +m: WU.U64, +mp: WU.U64, +hM: {SW.value(m) == 1n+bp : Nat}, +hinv: {1n+C.low(64n, Nat.mul(1n+bp, SW.value(mp))) == C.shift(64n, one) : Nat}, +h63: {Nat.is_lt(1n+bp, C.shift(63n, one)) == True{} : Bool}, +tl: WU.U64, +th: WU.U64, p: WU.U64 & WU.U64, +T: Nat, +eT: {Nat.add(SW.value(tl), C.shift(64n, SW.value(th))) == T : Nat}, +hT: {Nat.is_lt(T, Nat.mul(1n+bp, 1n+bp)) == True{} : Bool}, +eP: {Nat.add(SW.value(X.pfst(p)), C.shift(64n, SW.value(X.psnd(p)))) == Nat.mul(SW.value(X.mul(tl, mp)), 1n+bp) : Nat}) -> {Nat.mod(C.shift(64n, SW.value(X.redc_p(m, tl, th, p))), 1n+bp) == Nat.mod(T, 1n+bp) : Nat}:
181  match p:
182    case Tuple{+pl, +ph}:
183      rp_cong(one, h1, bp, m, mp, hM, hinv, h63, tl, th, pl, ph, T, eT, hT, eP)