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Proof step 2 from proof perm-shift-in2 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 3:
perm(y + z + a ', y + a ' + z), perm(x -1l a, y + z), a ∈ x, perm(y + z, x -1l a) ⊦ perm(x, y + a ' + z)

Rule argument

fma: perm(y + z + a ', y + a ' + z)

Additional information

Used simplifier rules: app: ⊦ perm(x + y, x + z) ↔ perm(y, z);%app-02: ⊦ perm(x + y, z + x) ↔ perm(y, z);%perm-one: ⊦ perm(x, a ') ↔ x = a ';%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: perm(y + z + a ', y + a ' + z)