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Proof step 11 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), # bits < n ⊦ lastn(n, fillsgn(n, bitsand(sgn(bits), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0))), bits = [], bits0 = []

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
⊦ 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 13:
true ∈ bits ∧ false ∈ bits → (∃ boolvar, n, boolvar0, bits0. bits = mklist(boolvar, n) + (boolvar0 + bits0) ∧ sgn(bits) = boolvar + boolvar0 + bits0 ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0), n = # fillsgn(n, bits), # bits < n ⊦ lastn(n, fillsgn(n, bitsand(sgn(bits), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0))), bits = [], 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] → [bits] rotate: F spec: bitopsaux inst: name: sgn-ex-01

Additional information

Used terms: bits