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Proof step 12 from proof le-2pot (previous step)

0 ≤ i, 0 ≤ j, 2 ^ (i + 1) ≤ j ⊦ 2 ^ i ≤ j / 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
2 ^ (i + 1) < 2 * 2 ^ i, j < 2 * 2 ^ i, 0 < 2 ^ i, 0 ≤ i, 0 ≤ j, 2 ^ (i + 1) ≤ j ⊦

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0); (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)