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Proof step 9 from proof perm-mklist (previous step)

x -1l a = mklist(a, n0), a ∈ x ⊦ x = a ' + (x -1l a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ x.first = a ∧ x ≠ [] → a ' + (x -1l a) = x
Proof step 11:
¬(x.first = a ∧ x ≠ []), x -1l a = mklist(a, n0), a ∈ x ⊦ x = a ' + (x -1l a)

Rule argument

spec: list-del inst: name: del1-first seq: ⊦ x.first = a ∧ x ≠ [] → a ' + (x -1l a) = x subst: [x, a] → [x, a] flags: rewrite

Additional information

Used terms: x, a