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Proof step 20 from proof band-011x-is-lastn (previous step)

bits = boolvar + bits1, # bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ i→n(i) = # bits0 + # bits, bits = [], bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(bits1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
int2bits(j) = bits0 + boolvar ' + bits1, # bits1 = i→n(i), 0 < i ⊦ bits2int(bitsand(boolvar ' + bits1, false ' + mklist(true, i→n(i)))) = bits2uint(bits1)

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ i;% ⊦ 0 < j → abs(j) = j;% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ m ≤ m + n;% ⊦ m + 1 ≠ 0;% ⊦ m = m + n ↔ n = 0;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ boolvar ' + bits ≠ [];% ⊦ 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;% ⊦ boolvar + bits = boolvar ' + bits;