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Proof step 32 from proof bitsand-app-zeros-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 33:
true ∈ bitsand(false ' + bits3, bits4), ∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3, bits4) + (boolvar ∧ boolvar0)') = sgn(bitsand(false ' + bits3, bits4) + (boolvar ∧ boolvar0)'), bits4 = [], true ∈ bits, true ∈ bitsand(false ' + bits3, bits4) ∧ false ∈ bitsand(false ' + bits3, bits4)
Proof step 36:
∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ true ∈ bitsand(false ' + bits3, bits4), sgn(bitsand(bits + false ' + bits3, bits4) + (boolvar ∧ boolvar0)') = sgn(bitsand(false ' + bits3, bits4) + (boolvar ∧ boolvar0)'), bits4 = [], true ∈ bits, true ∈ bitsand(false ' + bits3, bits4) ∧ false ∈ bitsand(false ' + bits3, bits4)

Rule argument

fma: true ∈ bitsand(false ' + bits3, bits4)

Additional information

Used formulas: true ∈ bitsand(false ' + bits3, bits4)