def addb

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64rint.bend:76

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/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/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/f64round.bend as FR

76def addb(+q: WU.U64, +b: Bool, +hq: {C.fits(63n, SW.value(q)) == True{} : Bool}) -> {SW.value(X.add(q, F.b64(b))) == Nat.add(SW.value(q), SF.b2n(b)) : Nat}:
77  +Q = SW.value(q)
78  e1 = WA.add_value(q, F.b64(b))
79  +e2 = Equal.cong(Nat, Nat, n => C.low(64n, Nat.add(Q, n)), SW.value(F.b64(b)), SF.b2n(b), b64v(b))
80  +hf = FR.fits_add1(63n, Q, SF.b2n(b), hq, b2n63(b))
81  +e3 = WW.low_fit(64n, Nat.add(Q, SF.b2n(b)), hf)
82  Equal.trans(Nat, SW.value(X.add(q, F.b64(b))), C.low(64n, Nat.add(Q, SW.value(F.b64(b)))), Nat.add(Q, SF.b2n(b)), e1, Equal.trans(Nat, C.low(64n, Nat.add(Q, SW.value(F.b64(b)))), C.low(64n, Nat.add(Q, SF.b2n(b))), Nat.add(Q, SF.b2n(b)), e2, e3))