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Proof step 45 from proof int2int-neg (previous step)

0 < 2 ^ i, 0 ≤ 2 ^ i, j ≤ 2 ^ i, j ≤ 0, j ≤ i + 2, j < i, 2 ^ i + j ≤ i, 0 < 4 * 2 ^ i + j, 0 ≤ 4 * 2 ^ i + j, j + 1 < 4 * 2 ^ i, 0 ≤ i, j ≤ i, j + 1 < 2 ^ i, j < 2 ^ i, j < 0, j < i + 2, 2 ^ i + j < i + 2, 2 ^ i + j ≤ i + 2, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ 0, j ≤ 3 * 2 ^ i, j < 3 * 2 ^ i, j < 4 * 2 ^ i, j ≤ 4 * 2 ^ i, j ≤ ~2 * 2 ^ i ⊦ 3 * 2 ^ i + j = 0, 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ i < 0 → (j ≤ i * i0 ↔ j + ~ i * i0 ≤ 0)

Rule argument

seq: ⊦ i < 0 → (j ≤ (* i) * i0 ↔ j + ~ i * i0 ≤ 0) subst: [i0, i, j] → [2 ^ i, ~2, j] rotate: F spec: int-mult inst: name: numleneg

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2 ^ i, ~2, j