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Proof step 14 from proof shiftright-not-pos-01 (previous step)

i < 0 ⊦ mklist(true, i→n(j)) + int2bits(i) = [], (mklist(true, i→n(j)) + int2bits(i)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 16:
mklist(true, i→n(j)) ≠ [], i < 0 ⊦ mklist(true, i→n(j)) + int2bits(i) = [], mklist(true, i→n(j)).first

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [int2bits(i), mklist(true, i→n(j))] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ int2bits(j) ≠ [];% ⊦ j < 0 → int2bits(j).first; Used terms: int2bits(i), mklist(true, i→n(j))