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Proof step 24 from proof shiftright-rec-pos (previous step)

0 ≤ i0 ⊦ bits2int(firstn(2, mklist(false, i→n(i0)) + false ' + false ' + true ')) = bits2int(firstn(1, mklist(false, i→n(i0)) + false '))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bits ≠ [] → firstn(1, bits) = bits.first '
Proof step 26:
mklist(false, i→n(i0)) + false ' ≠ [], 0 ≤ i0 ⊦ bits2int(firstn(2, mklist(false, i→n(i0)) + false ' + false ' + true ')) = bits2int((mklist(false, i→n(i0)) + false ').first ')

Rule argument

seq: ⊦ bits ≠ [] → firstn(1, bits) = bits.first ' subst: [bits] → [mklist(false, i→n(i0)) + false '] 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;% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(false, i→n(i0)) + false '