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Proof step 2 from proof Del-rec-other (previous step)

⊦ sdt[str0, tree] -- str = (sdt -- str)[str0, tree], str = str0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ sdt1 = sdt2 ↔ (∀ str. (str ∈ sdt1 ↔ str ∈ sdt2) ∧ sdt1[str] = sdt2[str])
Proof step 4:
⊦ str = str0, ∀ str1. (str1 ∈ sdt[str0, tree] -- str ↔ str1 ∈ (sdt -- str)[str0, tree]) ∧ (sdt[str0, tree] -- str)[str1] = (sdt -- str)[str0, tree][str1]

Rule argument

spec: directory-tree-base name: Extension seq: ⊦ sdt1 = sdt2 ↔ (∀ str. (str ∈ sdt1 ↔ str ∈ sdt2) ∧ sdt1[str] = sdt2[str]) subst: [sdt2, sdt1] → [(sdt -- str)[str0, tree], sdt[str0, tree] -- str] flags: <all paths>

Additional information

Used terms: (sdt -- str)[str0, tree], sdt[str0, tree] -- str