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Proof step 23 from proof shiftright-rec-neg (previous step)

⊦ j = 0, bits2int(firstn(1, mklist(true, i→n(j)) + true ')) = bits2int((mklist(true, i→n(abs(j) - 1)) + true ').first ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ bits ≠ [] → firstn(1, bits) = bits.first '
Proof step 25:
mklist(true, i→n(j)) + true ' ≠ [] ⊦ j = 0, bits2int((mklist(true, i→n(j)) + true ').first ') = bits2int((mklist(true, i→n(abs(j) - 1)) + true ').first ')

Rule argument

seq: ⊦ bits ≠ [] → firstn(1, bits) = bits.first ' subst: [bits] → [mklist(true, i→n(j)) + true '] rotate: F spec: list-del inst: bitlista name: firstN-one

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(true, i→n(j)) + true '