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Proof step 13 from proof bitsand-zero-in (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: and-rec-03 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used simplifier rules: and-zero-02: ⊦ bits ≠ [] → bitsand(false ', bits) = false ';% ⊦ # bits = 1 ∧ bits ≠ true ' → bits = false '; (forward)% ⊦ # boolvar ' = 0 +1;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ' ≠ [];% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0; Used terms: bits0, bits