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Proof step 52 from proof cast-help-comm (previous step)

# int2bits(j) ≤ i→n(i0), # 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), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))) = bits2int(mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits) subst: [bits, n, boolvar] → [int2bits(j), i→n(i0) - # int2bits(j), ¬ 0 ≤ j] rotate: F spec: int2bits inst: name: bits2int-mklist

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ int2bits(j).first ↔ j < 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ j < 0 → int2bits(j).first; Used terms: int2bits(j), i→n(i0) - # int2bits(j), ¬ 0 ≤ j