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Proof step 4 from proof validfield-put-statfield-01 (previous step)

rk .ref = jvmref, r ≠ jvmref ∨ rk .key ≠ sk0 ⊦ validfield(str, r, sk0, st[rk, val]) ↔ validfield(str, r, sk0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
rk = r0 -- sk, r0 = jvmref, r ≠ jvmref ∨ sk ≠ sk0 ⊦ validfield(str, r, sk0, st[rk, val]) ↔ validfield(str, r, sk0, st)

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r0, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r0, sk)]]