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Proof step 4 from proof Del-empty (previous step)

⊦ (∅ -- str)[str0] = (∅)[str0], str0 ∈ ∅ -- str

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str]
Proof step 6:
str0 = str ⊦ (∅ -- str)[str0] = (∅)[str0], str0 ∈ ∅ -- str

Rule argument

spec: directory-tree-base name: Del-at seq: ⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str] subst: [str, str0, sdt] → [str0, str, ∅] flags: <all paths>

Additional information

Used terms: str0, str, ∅