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Proof step 10 from proof Del-rec-other (previous step)

⊦ (sdt[str0, tree] -- str)[str1] = (sdt -- str)[str0, tree][str1], str = str0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str]
Proof step 12:
str1 = str ⊦ (sdt[str0, tree] -- str)[str1] = (sdt -- str)[str0, tree][str1], str = str0
Proof step 17:
⊦ sdt[str0, tree][str1] = (sdt -- str)[str0, tree][str1], str = str0, str1 = str

Rule argument

spec: directory-tree-base name: Del-at seq: ⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str] subst: [str, str0, sdt] → [str1, str, sdt[str0, tree]] flags: <all paths>

Additional information

Used terms: str1, str, sdt[str0, tree]