def esd

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64nrp.bend:62

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/src/math/natural.bend as M
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/math/typed/w64clz.bend as CLZ
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bl.bend as BL

62def esd(+sig: WU.U64, +h63: {C.fits(63n, SW.value(sig)) == True{} : Bool}) -> {Nat.sub(X.clz(sig), 1n) == Nat.sub(63n, M.bit_length(SW.value(sig))) : Nat}:
63  +hb = BL.bl_le(63n, SW.value(sig), h63, Nat.is_le(M.bit_length(SW.value(sig)), 63n), {==})
64  ec = CLZ.clz_value(sig)
65  Equal.trans(Nat, Nat.sub(X.clz(sig), 1n), Nat.sub(Nat.sub(64n, M.bit_length(SW.value(sig))), 1n), Nat.sub(63n, M.bit_length(SW.value(sig))), Equal.cong(Nat, Nat, z => Nat.sub(z, 1n), X.clz(sig), Nat.sub(64n, M.bit_length(SW.value(sig))), ec), Equal.trans(Nat, Nat.sub(Nat.sub(64n, M.bit_length(SW.value(sig))), 1n), Nat.sub(Nat.add(1n, Nat.sub(63n, M.bit_length(SW.value(sig)))), 1n), Nat.sub(63n, M.bit_length(SW.value(sig))), Equal.cong(Nat, Nat, z => Nat.sub(z, 1n), Nat.sub(64n, M.bit_length(SW.value(sig))), Nat.add(1n, Nat.sub(63n, M.bit_length(SW.value(sig)))), FR.sub_add_a(1n, 63n, M.bit_length(SW.value(sig)), hb)), N.add_sub_cancel(1n, Nat.sub(63n, M.bit_length(SW.value(sig))))))