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Proof step 21 from proof bib-on-bits (previous step)

# int2bits(i) ≤ 8, ~128 ≤ i, i ≤ 127 ⊦ i = bits2int(mklist(¬ 0 ≤ i, 8 - # int2bits(i)) + int2bits(i))

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(i), 8 - # int2bits(i), ¬ 0 ≤ i] rotate: F spec: int2bits inst: name: bits2int-mklist

Additional information

Used simplifier rules: ⊦ j < 0 → int2bits(j).first;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ int2bits(j).first ↔ j < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ bits2int(int2bits(i)) = i;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(i), 8 - # int2bits(i), ¬ 0 ≤ i