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Proof step 4 from proof perm-mklist-del (previous step)

∀ x, a. (perm(x, mklist(a, #oc(a, x)) + y0) ↔ perm(x -l a, y0)) ∨ a ∈ y0 ⊦ a = a0, perm(x, mklist(a, #oc(a, x)) + a0 ' + y0) ↔ a0 ∈ x ∧ perm((x -l a) -1l a0, y0), a ∈ y0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ perm(y, z + a ' + x) ↔ a ∈ y ∧ perm(y -1l a, z + x)
Proof step 6:
∀ x, a. (perm(x, mklist(a, #oc(a, x)) + y0) ↔ perm(x -l a, y0)) ∨ a ∈ y0 ⊦ a = a0, a0 ∈ x ∧ perm(x -1l a0, mklist(a, #oc(a, x)) + y0) ↔ a0 ∈ x ∧ perm((x -l a) -1l a0, y0), a ∈ y0

Rule argument

spec: inst: name: perm-rec seq: ⊦ perm(y, z + a ' + x) ↔ a ∈ y ∧ perm(y -1l a, z + x) subst: [x, a, z, y] → [y0, a0, mklist(a, #oc(a, x)), x] flags: rewrite, current

Additional information

Used terms: y0, a0, mklist(a, #oc(a, x)), x