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Proof step 4 from proof Del-rec-same (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 5:
⊦ str0 ∈ sdt[str, tree] -- str, (str0 ∈ sdt[str, tree] -- str ↔ str0 ∈ sdt -- str) ∧ (sdt[str, tree] -- str)[str0] = (sdt -- str)[str0]

Rule argument

fma: str0 ∈ sdt[str, tree] -- str

Additional information

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