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Proof step 18 from proof bitsand-zero-in (previous step)

bits0.last, false ∈ bits2 ∨ false ∈ bits0, ∀ bits0, bits1. # bits1 < #(bits2 + true ') → false ∈ bits1 ∨ false ∈ bits0 → bits0 = [] ∨ bits1 = [] ∨ false ∈ bitsand(bits1, bits0) ⊦ # bits0 = 1, bits0 = [], bits2 = [], false ∈ bitsand(bits2, bits0.butlast)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
bits0 = bits + boolvar ', boolvar, false ∈ bits2 ∨ false ∈ bits0, ∀ bits0, bits1. # bits1 < #(bits2 + true ') → false ∈ bits1 ∨ false ∈ bits0 → bits0 = [] ∨ bits1 = [] ∨ false ∈ bitsand(bits1, bits0) ⊦ # bits0 = 1, bits0 = [], bits2 = [], false ∈ bitsand(bits2, bits)

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar, bits] 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: bits0, boolvar, bits