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Proof step 40 from proof bitsand-app-zeros (previous step)

∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3, false ' + bits4) + (boolvar ∧ boolvar0)') = sgn(false ' + (boolvar ∧ boolvar0)'), true ∈ bits, true ∈ bitsand(false ' + bits3, false ' + bits4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(false ' + bits0)
Proof step 42:
¬(¬ true ∈ bitsand(bits + false ' + bits3, false ' + bits4) ∧ bitsand(bits + false ' + bits3, false ' + bits4) ≠ []), ∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3, false ' + bits4) + (boolvar ∧ boolvar0)') = sgn(false ' + (boolvar ∧ boolvar0)'), true ∈ bits, true ∈ bitsand(false ' + bits3, false ' + bits4)

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(false ' + bits0) subst: [bits0, bits] → [(boolvar ∧ boolvar0)', bitsand(bits + false ' + bits3, false ' + bits4)] rotate: F spec: bitopsaux inst: name: sgn-append-04

Additional information

Used terms: (boolvar ∧ boolvar0)', bitsand(bits + false ' + bits3, false ' + bits4)