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Proof step 8 from proof and-notone-01 (previous step)

bitsand(boolvar ', false ' + bits0) = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < #(boolvar + []) → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsand(bits, bits0) = bits0

Rule argument

name: and-rec-03 rotate: F subst: [bits0, bits] → [false ' + bits0, boolvar ']

Additional information

Used simplifier rules: and-zero-01: ⊦ bitsand(false ', boolvar ' + bits) = false ';%⊦ boolvar ' + bits = boolvar0 ' + bits0 ↔ (boolvar ↔ boolvar0) ∧ bits = bits0;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ' = boolvar0 ' + bits ↔ (boolvar ↔ boolvar0) ∧ bits = []; Used terms: false ' + bits0, boolvar '