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Proof step 6 from proof Del-rec-same (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str]
Proof step 8:
str0 = str ⊦ (sdt[str, tree] -- str)[str0] = (sdt -- str)[str0], str0 ∈ sdt -- str, str0 ∈ sdt[str, tree] -- str

Rule argument

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

Additional information

Used simplifier rules: ⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str]; (s)% ⊦ str ≠ str0 → (sdt -- str0)[str] = sdt[str]; (s) Used terms: str0, str, sdt[str, tree]