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Proof step 366 from proof bitsand-cast (previous step)

⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(sgn(bits1), bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0)))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 367:
⊦ true ∈ bits ∧ false ∈ bits → (∃ boolvar, n, boolvar0, bits0. bits = mklist(boolvar, n) + (boolvar0 + bits0) ∧ sgn(bits) = boolvar + boolvar0 + bits0 ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0)
Proof step 368:
true ∈ bits1 ∧ false ∈ bits1 → (∃ boolvar, n, boolvar0, bits0. bits1 = mklist(boolvar, n) + (boolvar0 + bits0) ∧ sgn(bits1) = boolvar + boolvar0 + bits0 ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0) ⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(sgn(bits1), bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0)))

Rule argument

seq: ⊦ true ∈ bits ∧ false ∈ bits → (∃ boolvar, n, boolvar0, bits0. bits = mklist(boolvar, n) + (boolvar0 + bits0) ∧ sgn(bits) = boolvar + boolvar0 + bits0 ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0) subst: [bits] → [bits1] rotate: F spec: bitopsaux inst: name: sgn-ex-01

Additional information

Used terms: bits1