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Proof step 35 from proof band-min (previous step)

j < 0 ∧ j ≠ ~1, # int2bits(i2 / 2) + 1 = #(int2bits((j - 1) / 2) + (~1 = j % 2)'), i0 + 2 ^ n→i(#(int2bits((j - 1) / 2) + (~1 = j % 2)')) ≤ 0, j ≤ 0, bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits((j - 1) / 2) + (~1 = j % 2)')) < i0, i2 < ~1, i2 < 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 ⊦ ~2 = i2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# int2bits(i2 / 2) = # int2bits((j - 1) / 2), bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits((j - 1) / 2) + (~1 = j % 2)')) < i0, i2 < ~1, i2 < 0, j < 0, 2 ^ (n→i(# int2bits(i2 / 2)) + 1) + 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 ⊦ ~2 = i2, j = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;