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Proof step 45 from proof cast-help-comm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, i→n(i0) ≤ (i→n(i0) - # int2bits(j)) + # int2bits(j) ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(restn((i→n(i0) - # int2bits(j)) + # int2bits(j) - i→n(i0), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j)))

Rule argument

Additional information

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