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Proof step 148 from proof uint2bits-add-high (previous step)

0 ≤ 2 ^ (i2 + 2), 0 < 2 ^ (i2 + 2), 2 + 2 ^ (1 + i2) < 2 ^ (i2 + 2), i1 * 2 ≤ 2 ^ (i2 + 2) + 1, 2 + 2 ^ (1 + i2) < i1 * 2 + 2 ^ (i2 + 2), 2 < i1 * 2 + 2 ^ (i2 + 2), 2 + 2 ^ (1 + i2) < 2 * (i1 + 1) + i2, 2 < 2 * (i1 + 1) + i2, 2 ^ (1 + i2) < i1 * 2 + 2 ^ (i2 + 2), 2 ^ (1 + i2) < i1 * 2, 1 < 2 ^ (i2 + 2), 0 ≤ i1, ~2 < i2, i1 * 2 < 2 ^ (i2 + 2), 0 < i1, 1 + 2 ^ (1 + i2) < i1 * 2, 0 < i1 * 2 + 2 ^ (i2 + 2), 0 ≤ 2 * (i1 + 1) + i2, 0 < 2 * (i1 + 1) + i2, 2 ^ (1 + i2) ≤ 2 ^ (i2 + 2), ∀ i0, j. i→n(i0) < i→n(i2 + 2) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ ~1 = i2, uint2bits(2 ^ (1 + i2) - i1) + ((1 - i1 * 2) % 2 ≠ 0)' = sgn(int2bits(1 - i1 * 2).rest), 2 ^ (i2 + 2) = i1 * 2, ¬ i1 ≤ 2 ^ i2 ∧ ¬ 2 ^ (1 + i2) < i1

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [1, i1 * 2, i] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: 1, i1 * 2, i