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Proof step 863 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, # bits0 ≤ (2 + # bits) + # bits2, bits0.first, # bits0 ≤ 2 + # bits + m, # bits0 ≤ 2 + # bits ⊦ boolvar ↔ boolvar0, bits0 = [], lastn(2 + # bits + m, mklist(bitsand(boolvar ' + boolvar0 ' + bits, bits0).first, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)) = lastn(2 + # bits + m, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 864:
⊦ bits ≠ [] ∧ bits0 ≠ [] → (bitsand(bits, bits0).first ↔ bits.first ∧ bits0.first)

Rule argument

name: and-first rotate: F subst: [bits0, bits] → [bits0, boolvar ' + boolvar0 ' + bits]

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ boolvar ' + bits ≠ []; Used terms: bits0, boolvar ' + boolvar0 ' + bits