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Proof step 4 from proof in-04 (previous step)

a ∈ x0, ∀ a, b. a ∈ x0 → a = b ∨ a ∈ x0 -1l b ⊦ a = b, a = a0, a ∈ (a0 ' + x0) -1l b

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a ∈ x0, ∀ a, b. a ∈ x0 → a = b ∨ a ∈ x0 -1l b ⊦ b = a0, a = b, a = a0, a ∈ (a0 ' + x0) -1l b

Rule argument

fma: b = a0

Additional information

Used simplifier rules: del1-y: ⊦ (a ' + x) -1l a = x;%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: b = a0