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Proof step 30 from proof sgn-last-04 (previous step)

∀ boolvar. ¬ boolvar ∨ false ∈ bits1 → sgn((true ' + bits1) + boolvar ') = sgn(true ' + bits1) + boolvar ' ⊦ sgn(true ' + bits1 + boolvar0 ') = sgn(true ' + bits1) + boolvar0 ', boolvar0 ∧ boolvar0 ∧ ¬ (¬ boolvar0) ∈ bits1

User applied rule case distinction

And obtained the following new goals

Proof step 31:
∀ boolvar. ¬ boolvar ∨ false ∈ bits1 → sgn((true ' + bits1) + boolvar ') = sgn(true ' + bits1) + boolvar ' ⊦ boolvar0, sgn(true ' + bits1 + boolvar0 ') = sgn(true ' + bits1) + boolvar0 '
Proof step 33:
∀ boolvar. ¬ boolvar ∨ false ∈ bits1 → sgn((true ' + bits1) + boolvar ') = sgn(true ' + bits1) + boolvar ' ⊦ boolvar0, sgn(true ' + bits1 + boolvar0 ') = sgn(true ' + bits1) + boolvar0 '
Proof step 35:
∀ boolvar. ¬ boolvar ∨ false ∈ bits1 → sgn((true ' + bits1) + boolvar ') = sgn(true ' + bits1) + boolvar ' ⊦ ¬ (¬ boolvar0) ∈ bits1, sgn(true ' + bits1 + boolvar0 ') = sgn(true ' + bits1) + boolvar0 '

Rule argument

pos: right 2

Proof step 30 from proof sgn-last-04 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information