def main_up

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64sqrt.bend:261

import Base
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/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

261def main_up(+one: Nat, +h1: {one == 1n : Nat}, +x: U32, +rd: U32, +m: U32, +pm: {m == U32{WD.mask(32n, 16n)} : U32}, p: {Nat.is_le(sq(v(rd)), v(x)) == True{} : Bool} & {Nat.is_lt(v(rd), WD.sc(16n, one)) == True{} : Bool}) -> {v(up32g(1n+U32.to_nat(U32.sub(m, rd)), x, rd, up_okg(x, rd, m), m)) == M.isqrt(v(x)) : Nat}:
262  (hsq, hbd) = p
263  +hle = le16(one, h1, rd, m, pm, hbd)
264  +es = U.sub_nat(m, rd, hle)
265  +hf = L.subst(Nat, z => {Nat.is_lt(Nat.sub(v(m), v(rd)), 1n+z) == True{} : Bool}, Nat.sub(v(m), v(rd)), v(U32.sub(m, rd)), Equal.sym(Nat, v(U32.sub(m, rd)), Nat.sub(v(m), v(rd)), es), N.lt_succ(Nat.sub(v(m), v(rd))))
266  main_fin(x, rd, m, 1n+v(U32.sub(m, rd)), up(1n+v(U32.sub(m, rd)), one, h1, x, rd, m, pm, hf, hle, hsq, up_okg(x, rd, m), {==}))