def ovle

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64round.bend:599

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/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

599# SoftFloat's carry test: 2^63 <= sig + 2^9
600def ovle(+one: Nat, +h1: {one == 1n : Nat}, +sig: WU.U64, +hS: {C.fits(63n, SW.value(sig)) == True{} : Bool}, +c: U32, +hc: {c == U32{WD.pw(32n, 31n)} : U32}) -> {X.le(WU.U64{0, c}, X.add(sig, WU.U64{512, 0})) == Bool.not(C.fits(63n, Nat.add(SW.value(sig), 512n))) : Bool}:
601  a1 = WA.add_value(sig, WU.U64{512, 0})
602  +ev1 = Equal.trans(Nat, SW.value(X.add(sig, WU.U64{512, 0})), C.low(64n, Nat.add(SW.value(sig), 512n)), Nat.add(SW.value(sig), 512n), a1, WW.low_fit(64n, Nat.add(SW.value(sig), 512n), fits_add1(63n, SW.value(sig), 512n, hS, {==})))
603  +ec = Equal.trans(Nat, C.shift(32n, v(c)), C.shift(32n, C.shift(31n, one)), C.shift(63n, one), Equal.cong(Nat, Nat, z => C.shift(32n, z), v(c), C.shift(31n, one), FB.pwv(31n, {==}, one, h1, c, hc)), Equal.sym(Nat, C.shift(63n, one), C.shift(32n, C.shift(31n, one)), WW.shift_comp(32n, 31n, one)))
604  l1 = WA.lt_value(X.add(sig, WU.U64{512, 0}), WU.U64{0, c})
605  +e2 = Equal.trans(Bool, Nat.is_lt(SW.value(X.add(sig, WU.U64{512, 0})), C.shift(32n, v(c))), Nat.is_lt(Nat.add(SW.value(sig), 512n), C.shift(32n, v(c))), Nat.is_lt(Nat.add(SW.value(sig), 512n), C.shift(63n, one)), Equal.cong(Nat, Bool, z => Nat.is_lt(z, C.shift(32n, v(c))), SW.value(X.add(sig, WU.U64{512, 0})), Nat.add(SW.value(sig), 512n), ev1), Equal.cong(Nat, Bool, z => Nat.is_lt(Nat.add(SW.value(sig), 512n), z), C.shift(32n, v(c)), C.shift(63n, one), ec))
606  +e3 = Equal.trans(Bool, X.lt(X.add(sig, WU.U64{512, 0}), WU.U64{0, c}), Nat.is_lt(Nat.add(SW.value(sig), 512n), C.shift(63n, one)), C.fits(63n, Nat.add(SW.value(sig), 512n)), Equal.trans(Bool, X.lt(X.add(sig, WU.U64{512, 0}), WU.U64{0, c}), Nat.is_lt(SW.value(X.add(sig, WU.U64{512, 0})), C.shift(32n, v(c))), Nat.is_lt(Nat.add(SW.value(sig), 512n), C.shift(63n, one)), l1, e2), lt_fit(63n, one, h1, Nat.add(SW.value(sig), 512n)))
607  Equal.cong(Bool, Bool, t => Bool.not(t), X.lt(X.add(sig, WU.U64{512, 0}), WU.U64{0, c}), C.fits(63n, Nat.add(SW.value(sig), 512n)), e3)