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def ilt1

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:91

import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqv.bend as F64sqv
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/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend as AQ

91# shift(32, isqrt nh) <= S < r0
92def ilt1(+one: Nat, +h1: {one == 1n : Nat}, +nh: WU.U64, +h62: {C.fits(62n, SW.value(nh)) == True{} : Bool}, +h60: {C.fits(60n, SW.value(nh)) == False{} : Bool}) -> {Nat.is_lt(SW.value(nh), Nat.mul(Nat.add(one, M.isqrt(SW.value(nh))), Nat.add(one, M.isqrt(SW.value(nh))))) == True{} : Bool}:
93  L.subst(Nat, z => {Nat.is_lt(SW.value(nh), Nat.mul(Nat.add(z, M.isqrt(SW.value(nh))), Nat.add(z, M.isqrt(SW.value(nh))))) == True{} : Bool}, 1n, one, Equal.sym(Nat, one, 1n, h1), AQ.ilt(SW.value(nh)))

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