def rp_lt

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64mont.bend:132

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
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

132def rp_lt(+one: Nat, +h1: {one == 1n : Nat}, +bp: Nat, +tl: WU.U64, +th: WU.U64, +mp: WU.U64, +pl: WU.U64, +ph: 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(pl), C.shift(64n, SW.value(ph))) == Nat.mul(SW.value(X.mul(tl, mp)), 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}) -> {Nat.is_lt(Nat.add(Nat.add(SW.value(th), SW.value(ph)), S.bit_value(X.add_over(tl, pl))), Nat.add(1n+bp, 1n+bp)) == True{} : Bool}:
133  rp_lt_g(one, h1, 1n+bp, {==}, tl, th, mp, pl, ph, T, hT, h63, rp_eq(one, bp, tl, th, mp, pl, ph, T, eT, eP, hinv))