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Proof step 10 from proof cast-law-shift-snd-l (previous step)

# int2bits(31) = m + 1 ∧ # int2bits(31) ≠ 0, 6 < # int2bits(31), 5 ≤ i, 0 < i, 0 ≤ i, i < n→i(m) ⊦ m = 1, m = 0, bits2int(int2bits(j0) + mklist(false, i→n(band(j, 31)))) = bits2int(int2bits(j0) + mklist(false, i→n(band(cast(i, j), 31))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: n0 < n ⊦ (* n) < m0 + (* n0) ↔ n - n0 < m0;% ⊦ m < n → n ≠ 0;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];