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Proof step 59 from proof band-min (previous step)

i0 = i + 1, # int2bits(i3) = # int2bits(i2), ~1 = ((i3 * 2 + j0) + 1) % 2, ~1 = ((i2 * 2 + j1) + 1) % 2, abs(j1) < 2, abs(j0) < 2, i3 * 2 + j0 < ~1, i2 * 2 + j1 < ~1, bits2int(bitsand(int2bits(i3), int2bits(i2))) < i / 2, j0 ≤ 0, i3 ≤ 0, i3 * 2 + j0 < 0, j1 ≤ 0, i2 ≤ 0, i2 * 2 + j1 < 0, 2 ^ (n→i(# int2bits(i2)) + 1) + i0 ≤ 0, i0 ≤ 0, ∀ i0, j, i1. i→n(i1) < i→n((i3 * 2 + j0) + 1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦ ~2 = i3 * 2 + j0, ~2 = i2 * 2 + j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 60:
# int2bits(i3) = # int2bits(i2), ~1 = ((i3 * 2 + j0) + 1) % 2, ~1 = ((i2 * 2 + j1) + 1) % 2, abs(j1) < 2, abs(j0) < 2, i3 * 2 + j0 < ~1, i2 * 2 + j1 < ~1, bits2int(bitsand(int2bits(i3), int2bits(i2))) < i / 2, j0 ≤ 0, i3 ≤ 0, i3 * 2 + j0 < 0, j1 ≤ 0, i2 ≤ 0, i2 * 2 + j1 < 0, 2 ^ (n→i(# int2bits(i2)) + 1) + i < 0, i < 0, ∀ i0, j, i1. i→n(i1) < i→n((i3 * 2 + j0) + 1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦ ~2 = i3 * 2 + j0, ~2 = i2 * 2 + j1

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ ~1 ↔ i < 0;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;