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Proof step 5 from proof notin-del (previous step)

∃ key0. key0 ∈ ri ⊖ key ∧ (ri ⊖ key)[key0] = adr ⊦ adr ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
key0.data?, key0 ∈ ri ⊦ inodekey(key0.ino) = key, key0 = key, (ri ⊖ key)[key0] ∈ ri

Rule argument

Additional information

Used simplifier rules: in-del-ro: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0);%at-del-ro-nodata: ⊦ key ∈ ri ∧ key ≠ key0 ∧ ¬ key.data? → (ri ⊖ key0)[key] = ri[key];%key ∈ ri ⊦ ri[key] ∈ ri; (s)