def hq

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64cmp.bend:328

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/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
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/u32laws.bend as LW

328def hq(+one: Nat, +h1: {one == 1n : Nat}, +xl: U32, +xh: U32, +yl: U32, +yh: U32, +nx: {SF.is_nan(F.Bits{xl, xh}) == False{} : Bool}, +ny: {SF.is_nan(F.Bits{yl, yh}) == False{} : Bool}) -> {Bool.and(Nat.is_eq(v(xl), v(yl)), Nat.is_eq(C.low(31n, v(xh)), C.low(31n, v(yh)))) == Cmp.is_eq(SF.mag_cmp(F.Bits{xl, xh}, F.Bits{yl, yh})) : Bool}:
329  +e1 = WW.eq_limbs(32n, v(xl), C.low(31n, v(xh)), v(yl), C.low(31n, v(yh)), LW.vb(xl), LW.vb(yl))
330  +e2 = Equal.trans(Bool, Nat.is_eq(Nat.add(v(xl), C.shift(32n, C.low(31n, v(xh)))), Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh))))), Nat.is_eq(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh))))), Nat.is_eq(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), Nat.add(SF.frac(F.Bits{yl, yh}), C.shift(52n, SF.efield(F.Bits{yl, yh})))), Equal.cong(Nat, Bool, t => Nat.is_eq(t, Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh))))), Nat.add(v(xl), C.shift(32n, C.low(31n, v(xh)))), Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), magQ(xl, xh)), Equal.cong(Nat, Bool, t => Nat.is_eq(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), t), Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh)))), Nat.add(SF.frac(F.Bits{yl, yh}), C.shift(52n, SF.efield(F.Bits{yl, yh}))), magQ(yl, yh)))
331  +e3 = Equal.cong(Cmp, Bool, t => Cmp.is_eq(t), Nat.cmp(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), Nat.add(SF.frac(F.Bits{yl, yh}), C.shift(52n, SF.efield(F.Bits{yl, yh})))), SF.mag_cmp(F.Bits{xl, xh}, F.Bits{yl, yh}), Equal.sym(Cmp, SF.mag_cmp(F.Bits{xl, xh}, F.Bits{yl, yh}), Nat.cmp(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), Nat.add(SF.frac(F.Bits{yl, yh}), C.shift(52n, SF.efield(F.Bits{yl, yh})))), magc(one, h1, xl, xh, yl, yh, nx, ny)))
332  Equal.trans(Bool, Bool.and(Nat.is_eq(v(xl), v(yl)), Nat.is_eq(C.low(31n, v(xh)), C.low(31n, v(yh)))), Nat.is_eq(Nat.add(v(xl), C.shift(32n, C.low(31n, v(xh)))), Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh))))), Cmp.is_eq(SF.mag_cmp(F.Bits{xl, xh}, F.Bits{yl, yh})), e1, Equal.trans(Bool, Nat.is_eq(Nat.add(v(xl), C.shift(32n, C.low(31n, v(xh)))), Nat.add(v(yl), C.shift(32n, C.low(31n, v(yh))))), Nat.is_eq(Nat.add(SF.frac(F.Bits{xl, xh}), C.shift(52n, SF.efield(F.Bits{xl, xh}))), Nat.add(SF.frac(F.Bits{yl, yh}), C.shift(52n, SF.efield(F.Bits{yl, yh})))), Cmp.is_eq(SF.mag_cmp(F.Bits{xl, xh}, F.Bits{yl, yh})), e2, e3))