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Proof step 31 from proof ac-mode-01 (previous step)

⊦ (addclass(class, fis, st)[_mode]) = st[_mode], _mode .key ∈ fis

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
_mode = r -- sk ⊦ (addclass(class, fis, st)[_mode]) = st[_mode], sk ∈ fis

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [_mode, r, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (_mode, r, sk)]]