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Proof step 3 from proof initsubset-mode-02 (conclusion)

⊦ init⊆(str, st[_mode, val], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ init⊆(str, st, st0) ↔ (∀ class. initdone(class, st) → initdone(class, st0)) ∧ (∀ class. initerror(class, st) → initerror(class, st0)) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0)) ∧ (∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0))
Proof step 2:
⊦ sk ∈ statfields(class) → (validstatfield(str, sk, st[_mode, val]) ↔ validstatfield(str, sk, st))

Rule argument

[crewrite-arg: initsubset-def , F , [st0, st, str] → [st, st[_mode, val], str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ initdone(class1, st[_mode, val]) ↔ initdone(class1, st)], [CSIMPSEQ : ⊦ initerror(class1, st[_mode, val]) ↔ initerror(class1, st)])], [EXTRATERMS : (st, st[_mode, val], str)]]