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Proof step 93 from proof band-min (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 94:
# int2bits(i2 / 2) = # int2bits(i / 2), i2 < ~1, i2 < 0, i < ~1, 2 ^ (n→i(# int2bits(i / 2)) + 1) + i0 ≤ 0, i < 0, bits2int(bitsand(int2bits(i2 / 2), int2bits(i / 2))) < i0 / 2, i0 < 0, 2 ^ (n→i(# int2bits(i / 2)) + 1) + i0 < i0 / 2 + 2 ^ n→i(# int2bits(i / 2)), 0 < i0 / 2 + 2 ^ n→i(# int2bits(i / 2)), ∀ i0, j, i1. i→n(i1) < i→n(i2 + 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 = i2, ~2 = i, ~1 = (i2 + 1) % 2 ∧ ~1 = (i + 1) % 2

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ ¬ i ≤ j ↔ j < i;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i < j ↔ j ≤ i;