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Proof step 31 from proof exin2pot (previous step)

j1 < 2, i0 < 2 ^ i * 2, 0 < i0 * 2 + j1, 0 < i0, 0 ≤ j1, 2 ^ i ≤ i0, 0 ≤ i0, 0 ≤ i, 4 * 2 ^ i ≤ i0 * 2 + j1, ∀ j0. i→n(j0) < i→n(i0 * 2 + j1) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ i0 * 2 + j1 = 0, i0 * 2 + j1 = 1

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modlep seq: j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [2, 2 * 2 ^ i, i0, j1]

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j → (j ≤ i ↔ false); (as)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → ¬ j < i; (s) Used terms: 2, 2 * 2 ^ i, i0, j1