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Proof step 70 from proof band-011x-pos (previous step)

j = i1 * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 < 2, bits2uint(bits) = i1 % 2 ^ i0, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(i1)) = false ' + bits, j1 = 1, 0 ≤ i0, 0 ≤ j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ ~1 = i0, j = 1, bits2uint(bits) * 2 + 1 = j % (2 ^ i0 * 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
bits2uint(bits) = i1 % 2 ^ i0, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(i1)) = false ' + bits, 0 ≤ i0, 0 < i1, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ bits2uint(bits) * 2 + 1 = (i1 * 2 + 1) % (2 ^ i0 * 2), ~1 = i0, i1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;