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Proof step 50 from proof uint2bits-add-low (previous step)

j0 < 2 ^ i, 1 < i1 * 2 + i, 1 < i1 * 2 + 2 ^ (i - 1), 2 < 2 ^ i, 0 < i1 * 2 + j0, 1 < (i1 * 2 + j0) + j0, 0 ≤ 2 ^ (i - 1), i1 * 2 + j0 < 2 ^ i, 2 < (i1 * 2 + j0) + i, 0 < 2 ^ (i - 1), 0 < i, i1 * 2 + j0 ≤ 2 ^ (i - 1) + 1, 2 < (i1 * 2 + j0) + 2 ^ (i - 1), i1 * 2 + j0 ≤ 2 ^ i, 2 < (i1 * 2 + j0) + 2 ^ i, 0 ≤ 2 ^ i, i1 * 2 + j0 ≤ 2 ^ i + 1, 2 ^ (i - 2) < i1, 0 ≤ j0, j0 < 2, 0 ≤ i1, 1 < i1 * 2 + j0, 0 < (i1 * 2 + j0) + j0, 0 ≤ (i1 * 2 + j0) + j0, 0 ≤ (i1 * 2 + j0) + i, 0 ≤ (i1 * 2 + j0) + 2 ^ (i - 1), 0 ≤ (i1 * 2 + j0) + 2 ^ i, 0 ≤ i1 * 2 + i, 0 < i1 * 2 + i, 0 < i1 * 2 + 2 ^ (i - 1), 0 < 2 ^ i, j0 + 1 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ abs(j) ≤ 2 ^ (i0 - 1) → uint2bits(j + 2 ^ i0) = false ' + fillsgn(i→n(i0), int2bits(j)) ⊦ i = 1, 1 = i1 * 2 + j0, uint2bits(2 ^ (i - 1) - i1) + (~1 = (1 - i1 * 2 + j0) % 2)' = false ' + fillsgn(i→n(i), int2bits(1 - i1 * 2 + j0))

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] → [i, 2, i2] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i, 2, i2