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Proof step 8 from proof perm-last-rec (previous step)

∀ x, a. perm(x, y0 + a ') ↔ a ∈ x ∧ perm(x -1l a, y0) ⊦ a0 ∈ x ∧ perm(x -1l a0, y0 + a ') ↔ a ∈ x ∧ a0 ∈ x -1l a ∧ perm((x -1l a0) -1l a, y0)

User applied rule all left

And obtained the following new goals

Proof step 9:
perm(x -1l a0, y0 + a ') ↔ a ∈ x -1l a0 ∧ perm((x -1l a0) -1l a, y0) ⊦ a0 ∈ x ∧ perm(x -1l a0, y0 + a ') ↔ a ∈ x ∧ a0 ∈ x -1l a ∧ perm((x -1l a0) -1l a, y0)

Rule argument

pos: left 1 terms: x -1l a0, a abort: F discard: T computed: T

Additional information

Used terms: x -1l a0, a