def n3b

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64norm.bend:151

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/f64.bend as F
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/nat.bend as N
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/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR

151def n3b(+one: Nat, +h1: {one == 1n : Nat}, +ea: Nat, +fa: WU.U64, +E: Nat, +Fr: Nat, +hea: {ea == E : Nat}, +hfa: {SW.value(fa) == Fr : Nat}, +hF: {C.fits(52n, Fr) == True{} : Bool}, +hnz: {Bool.and(Nat.is_eq(E, 0n), Nat.is_eq(Fr, 0n)) == False{} : Bool}) -> {C.fits(52n, SW.value(F.norm_f(ea, fa))) == False{} : Bool}:
152  match ea:
153    case 0n:
154      +ez = ez0(E, hea)
155      +hz = L.subst(Bool, t => {Bool.and(t, Nat.is_eq(Fr, 0n)) == False{} : Bool}, Nat.is_eq(E, 0n), True{}, ez, hnz)
156      L.subst(Nat, z => {C.fits(52n, z) == False{} : Bool}, C.shift(Nat.sub(X.clz(fa), 11n), Fr), SW.value(X.shl(fa, Nat.sub(X.clz(fa), 11n))), Equal.sym(Nat, SW.value(X.shl(fa, Nat.sub(X.clz(fa), 11n))), C.shift(Nat.sub(X.clz(fa), 11n), Fr), sub_val(fa, Fr, hfa, hF, hz)), sub_nfit(fa, Fr, hfa, hF, hz))
157    case 1n+ +p:
158      +hFv = L.subst(Nat, z => {C.fits(52n, z) == True{} : Bool}, Fr, SW.value(fa), Equal.sym(Nat, SW.value(fa), Fr, hfa), hF)
159      +nf = Equal.trans(Bool, C.fits(52n, C.shift(52n, one)), Nat.is_lt(C.shift(52n, one), C.shift(52n, one)), False{}, Equal.sym(Bool, Nat.is_lt(C.shift(52n, one), C.shift(52n, one)), C.fits(52n, C.shift(52n, one)), FR.lt_fit(52n, one, h1, C.shift(52n, one))), N.lt_irrefl(C.shift(52n, one)))
160      +hle = L.subst(Nat, z => {Nat.is_le(C.shift(52n, one), z) == True{} : Bool}, Nat.add(C.shift(52n, one), SW.value(fa)), Nat.add(SW.value(fa), C.shift(52n, one)), NA.add_comm(C.shift(52n, one), SW.value(fa)), N.le_add_right(C.shift(52n, one), SW.value(fa)))
161      L.subst(Nat, z => {C.fits(52n, z) == False{} : Bool}, Nat.add(SW.value(fa), C.shift(52n, one)), SW.value(X.add(fa, WU.U64{0, 1048576})), Equal.sym(Nat, SW.value(X.add(fa, WU.U64{0, 1048576})), Nat.add(SW.value(fa), C.shift(52n, one)), hid(one, h1, fa, hFv, 1048576, {==})), FR.nfit(52n, C.shift(52n, one), Nat.add(SW.value(fa), C.shift(52n, one)), hle, nf))