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Proof step 46 from proof validstatfields-put-other-statfield (previous step)

sk ∈ statfields(class0), initdone(class0, st[jvmref -- mkfs(class, ty, fieldvar) ', val]), tdname∃(str, class0), ∀ class, sk. tdname∃(str, class) ∧ initdone(class, st) ∧ sk ∈ statfields(class) → validstatfield(str, sk, st) ⊦ class = `java.lang.Object' .class, tdname∃(str, class), validstatfield(str, sk, st[jvmref -- mkfs(class, ty, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ is_indexkey(sk) → ¬ sk ∈ statfields(class)
Proof step 45:
¬ is_indexkey(sk), sk ∈ statfields(class0), initdone(class0, st[jvmref -- mkfs(class, ty, fieldvar) ', val]), tdname∃(str, class0), ∀ class, sk. tdname∃(str, class) ∧ initdone(class, st) ∧ sk ∈ statfields(class) → validstatfield(str, sk, st) ⊦ class = `java.lang.Object' .class, tdname∃(str, class), validstatfield(str, sk, st[jvmref -- mkfs(class, ty, fieldvar) ', val])

Rule argument

[x0lemmaarg: spec-name: addfuns instance-name: lemma-name: statfields-index-01 antecedent: succedent: is_indexkey(sk) → ¬ sk ∈ statfields(class) substlist: [class, sk] → [class0, sk] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (class0, sk)]]