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Proof step 57 from proof cast-help-comm (previous step)

¬ i→n(i) ≤ #(mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j)), # int2bits(j) ≤ i→n(i0), # int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, ¬ 0 ≤ j → j < 0 ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
# int2bits(j) ≤ i→n(i0), # int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, (i→n(i0) - # int2bits(j)) + # int2bits(j) < i→n(i), ¬ 0 ≤ j → j < 0 ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))) = j

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;