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Proof step 4 from proof succ-zeros-01 (previous step)

∀ bits1, bits. # bits1 < # bits0 → true → (bits + bits1)+1 = bits +1 + bitsinvert(bits1) ∨ false ∈ bits1 ⊦ (bits + bits0)+1 = bits +1 + bitsinvert(bits0), false ∈ bits0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 5:
⊦ bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar ')
Proof step 6:
bits0 ≠ [] → (∃ bits1, boolvar. bits0 = bits1 + boolvar '), ∀ bits1, bits. # bits1 < # bits0 → true → (bits + bits1)+1 = bits +1 + bitsinvert(bits1) ∨ false ∈ bits1 ⊦ (bits + bits0)+1 = bits +1 + bitsinvert(bits0), false ∈ bits0

Rule argument

seq: ⊦ bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar ') subst: [bits] → [bits0] rotate: F spec: list inst: bitlista name: lastdiv

Additional information

Used terms: bits0