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Proof step 37 from proof band-min (previous step)

j = i + 1, # int2bits(i2 / 2) = # int2bits(i / 2), bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits(i / 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# int2bits(i2 / 2) = # int2bits(i / 2), bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits(i / 2) + (~1 = (i + 1) % 2)')) < i0, i2 < ~1, i2 < 0, i < ~1, 2 ^ (n→i(# int2bits(i / 2)) + 1) + i0 ≤ 0, i < 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, ~2 = i

Rule argument

Additional information

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