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Proof step 7 from proof bits2uint-not-zero (previous step)

bits2uint(bits) = 0, true ∈ bits, ∀ bits0. # bits0 < # bits → bits2uint(bits0) = 0 ∧ true ∈ bits0 → false ⊦ bits = [], bits.last

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
bits = bits1 + boolvar ', bits2uint(bits) = 0, true ∈ bits, ∀ bits0. # bits0 < # bits → bits2uint(bits0) = 0 ∧ true ∈ bits0 → false ⊦ bits = [], boolvar

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar, bits1] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits, boolvar, bits1