def le_qs

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/w64dmrem.bend:41

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64dm.bend as DM

41def le_qs(+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(DM.X96(WU.U64{al, ah}, 0), Nat.mul(1n+DM.v(e), SW.value(WU.U64{bl, bh}))) == True{} : Bool}) -> {Nat.is_le(Nat.mul(DM.v(X.q_start(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e)), SW.value(WU.U64{bl, bh})), SW.value(WU.U64{al, ah})) == True{} : Bool}:
42  L.subst(U32, z => {Nat.is_le(Nat.mul(DM.v(z), SW.value(WU.U64{bl, bh})), SW.value(WU.U64{al, ah})) == True{} : Bool}, DM.QS(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295), X.q_start(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e), Equal.sym(U32, X.q_start(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e), DM.QS(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e, 4294967295), DM.impl_qs(WU.U64{al, ah}, 0, WU.U64{bl, bh}, e)), DM.dm_le(one, h1, al, ah, bl, bh, e, hz, he))