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Proof step 68 from proof bitsand-cast (previous step)

n = # fillsgn(n, boolvar ' + boolvar0 ' + bits1), sgn(boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, bits0.first, # bits0 ≤ 2 + # bits1, # bits0 < n, 2 + # bits1 < n, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) = mklist(bitsand(boolvar ' + boolvar0 ' + bits1, bits0).first, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), bits0 = [], boolvar ↔ boolvar0, bitsand(boolvar ' + boolvar0 ' + bits1, bits0).first ↔ boolvar, boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ bits ≠ [] ∧ bits0 ≠ [] → (bitsand(bits, bits0).first ↔ bits.first ∧ bits0.first)

Rule argument

name: and-first rotate: F subst: [bits0, bits] → [bits0, boolvar ' + boolvar0 ' + bits1]

Additional information

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