def dm_le

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64dm.bend:216

import Base
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/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

216def dm_le(+one: Nat, +h1: {one == 1n : Nat}, +al: U32, +ah: U32, +bl: U32, +bh: U32, +e: U32, +hz: {U32.is_zero(bh) == False{} : Bool}, +he: {Nat.is_lt(X96(WU.U64{al, ah}, 0), Nat.mul(1n+v(e), SW.value(WU.U64{bl, bh}))) == True{} : Bool}) -> {Nat.is_le(Nat.mul(v(QS(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295)), SW.value(WU.U64{bl, bh})), SW.value(WU.U64{al, ah})) == True{} : Bool}:
217  +vbv = SW.value(WU.U64{bl, bh})
218  +hX = dm_hx(one, h1, al, ah, bl, bh, hz)
219  pr = qs_pair(one, h1, WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295, {==}, hX, he)
220  L.subst(Nat, z => {Nat.is_le(Nat.mul(v(QS(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295)), vbv), z) == True{} : Bool}, X96(WU.U64{al, ah}, 0), SW.value(WU.U64{al, ah}), x96_0(WU.U64{al, ah}), qle_fin(X96(WU.U64{al, ah}, 0), v(QS(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295)), vbv, pr))