def plus1

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqv.bend:72

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

72def plus1(+one: Nat, +h1: {one == 1n : Nat}, +nh: WU.U64, +h62: {C.fits(62n, SW.value(nh)) == True{} : Bool}, +h60: {C.fits(60n, SW.value(nh)) == False{} : Bool}) -> {Nat.add(v(X.lo(X.isqrt(nh))), v(1)) == 1n+M.isqrt(SW.value(nh)) : Nat}:
73  Equal.trans(Nat, Nat.add(v(X.lo(X.isqrt(nh))), 1n), Nat.add(M.isqrt(SW.value(nh)), 1n), 1n+M.isqrt(SW.value(nh)), Equal.cong(Nat, Nat, z => Nat.add(z, 1n), v(X.lo(X.isqrt(nh))), M.isqrt(SW.value(nh)), lo_iv(one, h1, nh, h62, h60)), Equal.trans(Nat, Nat.add(M.isqrt(SW.value(nh)), 1n), 1n+Nat.add(M.isqrt(SW.value(nh)), 0n), 1n+M.isqrt(SW.value(nh)), N.add_succ(M.isqrt(SW.value(nh)), 0n), N.succ_cong(Nat.add(M.isqrt(SW.value(nh)), 0n), M.isqrt(SW.value(nh)), N.add_zero(M.isqrt(SW.value(nh))))))