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Proof step 9 from proof shift-03 (previous step)

a ∈ y, a ∈ y -1l a0 → (perm(x1 + a ' + x0, y -1l a0) ↔ perm(x1 + x0, (y -1l a0) -1l a)) ⊦ a0 ∈ y ∧ perm(x1 + a ' + x0, y -1l a0) ↔ a0 ∈ y -1l a ∧ perm(x1 + x0, (y -1l a0) -1l a)

User applied rule cut formula

And obtained the following new goals

Proof step 10:
a ∈ y -1l a0, a ∈ y, a ∈ y -1l a0 → (perm(x1 + a ' + x0, y -1l a0) ↔ perm(x1 + x0, (y -1l a0) -1l a)) ⊦ a0 ∈ y ∧ perm(x1 + a ' + x0, y -1l a0) ↔ a0 ∈ y -1l a ∧ perm(x1 + x0, (y -1l a0) -1l a)
Proof step 12:
a ∈ y, a ∈ y -1l a0 → (perm(x1 + a ' + x0, y -1l a0) ↔ perm(x1 + x0, (y -1l a0) -1l a)) ⊦ a ∈ y -1l a0, a0 ∈ y ∧ perm(x1 + a ' + x0, y -1l a0) ↔ a0 ∈ y -1l a ∧ perm(x1 + x0, (y -1l a0) -1l a)

Rule argument

fma: a ∈ y -1l a0

Additional information

Used formulas: a ∈ y -1l a0