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Proof step 8 from proof succ-first-01 (previous step)

boolvar ' +1 + bitsinvert(bits0) = boolvar0 ' + bits, true ∈ bits ⊦ boolvar0 ↔ boolvar, false ∈ bits0, ¬ (¬ boolvar0) ∈ bits0 ∧ ¬ boolvar0 ∈ boolvar ' +1

User applied rule cut formula

And obtained the following new goals

Proof step 9:
boolvar, boolvar ' +1 + bitsinvert(bits0) = boolvar0 ' + bits, true ∈ bits ⊦ boolvar0 ↔ boolvar, false ∈ bits0, ¬ (¬ boolvar0) ∈ bits0 ∧ ¬ boolvar0 ∈ boolvar ' +1

Rule argument

fma: boolvar

Additional information

Used simplifier rules: succ-one: ⊦ false ' +1 = true ';%inv-in-02: ⊦ true ∈ bitsinvert(bits) ↔ false ∈ bits;%⊦ boolvar ' + bits = boolvar0 ' + bits0 ↔ (boolvar ↔ boolvar0) ∧ bits = bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0; Used formulas: boolvar