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Proof step 76 from proof cast-help-comm (previous step)

i→n(i0) ≤ #(mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j))), i→n(i) ≤ # int2bits(j), i < i0, 0 < i, 0 < i0, 1 < i0, i ≤ i0 ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int (restn (#(mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j))) - i→n(i0), mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j)))), i0 = 0, i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
i→n(i) ≤ # int2bits(j), i < i0, 0 < i, 0 < i0, 1 < i0, i ≤ i0, i→n(i0) ≤ (i→n(i0) - i→n(i)) + i→n(i) ⊦ i0 = 0, i = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(restn((i→n(i0) - i→n(i)) + i→n(i) - i→n(i0), mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j))))

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n ≤ # bits → # lastn(n, bits) = n;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;