def bal.hi

bend-kit-collections@0.1.4.1 · PROOF.bend:1571

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/omap.bend as O
import bend-kit-collections@0.1.4.1/nat_order.bend as Ord

1571def bal.hi(
1572  -K: Data, -V: Data, +k: K, +v: V, +lo: O.OMap<K, V>, +hi: O.OMap<K, V>, +hi2: O.OMap<K, V>,
1573  +ok: {Laws.weight_ok(W(K, V, lo), W(K, V, hi)) == True{} : Bool},
1574  wbl: {WB(K, V, lo) == True{} : Bool},
1575  +pw: {PW(K, V, W(K, V, hi), hi2) == True{} : Bool}
1576) -> {PW(K, V, Nat.add(W(K, V, lo), W(K, V, hi)), Laws.g_balance(K, V, k, v, lo, hi2)) == True{} : Bool}:
1577  +a = W(K, V, lo)
1578  +c = W(K, V, hi)
1579  +c2 = W(K, V, hi2)
1580  +nr = MBool.eq_true_of_and_right(WB(K, V, hi2), Ord.near(c, c2), pw)
1581  +n1 = MBool.eq_true_of_and_left(Nat.is_le(c, 1n+c2), Nat.is_le(c2, 1n+c), nr)
1582  +n2 = MBool.eq_true_of_and_right(Nat.is_le(c, 1n+c2), Nat.is_le(c2, 1n+c), nr)
1583  MBool.and_eq_true(WB(K, V, Laws.g_balance(K, V, k, v, lo, hi2)), Ord.near(Nat.add(a, c), W(K, V, Laws.g_balance(K, V, k, v, lo, hi2))), bal.wb(K, V, k, v, lo, hi2, wbl, MBool.eq_true_of_and_left(WB(K, V, hi2), Ord.near(c, c2), pw),
1584      Ord.almhi.w0(a, c, c2, Ord.wok_l(a, c, ok), Ord.wok_r(a, c, ok), n1, n2)), bal.hi.near(K, V, k, v, lo, hi, hi2, n1, n2))