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Proof step 18 from proof band-011x-pos (previous step)

1 < #(false ' + mklist(true, i→n(i))) ∧ 1 < #(false ' + true '), 0 < i, ∀ j0, i. i→n(j0) < i→n(1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int (bitsand((false ' + mklist(true, i→n(i))).butlast, (false ' + true ').butlast) + ((false ' + mklist(true, i→n(i))).last ∧ (false ' + true ').last)) = 1 % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
0 < i, ∀ j0, i. i→n(j0) < i→n(1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand((false ' + mklist(true, i→n(i))).butlast, false ') + (false ' + mklist(true, i→n(i))).last ') = 1 % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (bits + boolvar ').last ↔ boolvar;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + boolvar ').butlast = bits;