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Proof step 5 from proof Del-rec-same (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ (sdt[str, tree] -- str)[str0] = (sdt -- str)[str0], str0 ∈ sdt[str, tree] -- str, str0 ∈ sdt -- str

Rule argument

Additional information

Used simplifier rules: ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws)% ⊦ str ∈ sdt -- str0 ↔ str ≠ str0 ∧ str ∈ sdt; (ws)