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Proof step 15 from proof band-011x-is-lastn (previous step)

#(false ' + mklist(true, i→n(i))) ≤ # bits ∧ false ' + mklist(true, i→n(i)) ≠ [] ∧ ¬ (false ' + mklist(true, i→n(i))).first, int2bits(j) = bits0 + bits, # bits = i→n(i) + 1, i→n(i) < # bits0 + # bits, 0 < i ⊦ i→n(i) = # bits0 + # bits, bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(lastn(i→n(i), bits0 + bits))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(lastn(i→n(i), bits0 + bits)), i→n(i) = # bits0 + # bits, bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j → abs(j) = j;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ m ≤ m;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward)% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];