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Proof step 4 from proof bits2uint-split (previous step)

∀ bits1, bits. # bits1 < # bits0 → true → bits2uint(bits + bits1) = bits2uint(bits) * 2 ^ n→i(# bits1) + bits2uint(bits1) ∨ bits1 = [] ⊦ bits0 = [], bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ bits ≠ [] ↔ (∃ bits0, boolvar. bits = bits0 + boolvar ')
Proof step 6:
∀ bits1, bits. # bits1 < # bits0 → true → bits2uint(bits + bits1) = bits2uint(bits) * 2 ^ n→i(# bits1) + bits2uint(bits1) ∨ bits1 = [] ⊦ ∀ bits1, boolvar. bits0 ≠ bits1 + boolvar ', bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)

Rule argument

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

Additional information

Used terms: bits0