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Proof step 1 from proof del (conclusion)

⊦ perm(x, a ' + y) ↔ a ∈ x ∧ perm(x -1l a, y)

User applied rule cut formula

And obtained the following new goals

Proof step 2:
a ∈ x ⊦ perm(x, a ' + y) ↔ a ∈ x ∧ perm(x -1l a, y)

Rule argument

fma: a ∈ x

Additional information

Used simplifier rules: in-01: ⊦ ¬ a ∈ x → ¬ perm(x, a ' + y);%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a ∈ x