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Proof step 1 from proof Del-empty (conclusion)

⊦ ∅ -- str = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ sdt1 = sdt2 ↔ (∀ str. (str ∈ sdt1 ↔ str ∈ sdt2) ∧ sdt1[str] = sdt2[str])
Proof step 3:
⊦ ∀ str0. (str0 ∈ ∅ -- str ↔ str0 ∈ ∅) ∧ (∅ -- str)[str0] = (∅)[str0]

Rule argument

spec: directory-tree-base name: Extension seq: ⊦ sdt1 = sdt2 ↔ (∀ str. (str ∈ sdt1 ↔ str ∈ sdt2) ∧ sdt1[str] = sdt2[str]) subst: [sdt2, sdt1] → [∅, ∅ -- str] flags: <all paths>

Additional information

Used terms: ∅, ∅ -- str