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Proof step 40 from proof validstatfields-put-other-statfield (previous step)

fs ' ∈ statfields(class0), initdone(class0, st), 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, fs ', st[jvmref -- mkfs(class, ty, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ sk ≠ sk0 ∧ ( ¬ is_fskey(sk) ∨ sk .fs .type ≠ void_type ∨ sk .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(sk0) ∨ sk .fs ≠ mkfs(sk0 .fs .class, void_type, `initstate' .field))) → (validstatfield(str, sk0, st[jvmref -- sk, val]) ↔ validstatfield(str, sk0, st))
Proof step 35:
¬ ( mkfs(class, ty, fieldvar) ' ≠ fs ' ∧ ( ¬ is_fskey(mkfs(class, ty, fieldvar) ') ∨ mkfs(class, ty, fieldvar) ' .fs .type ≠ void_type ∨ mkfs(class, ty, fieldvar) ' .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(fs ') ∨ mkfs(class, ty, fieldvar) ' .fs ≠ mkfs(fs ' .fs .class, void_type, `initstate' .field)))), fs ' ∈ statfields(class0), initdone(class0, st), 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, fs ', st[jvmref -- mkfs(class, ty, fieldvar) ', val])
Proof step 39:
mkfs(class, ty, fieldvar) ' ≠ fs ' ∧ ( ¬ is_fskey(mkfs(class, ty, fieldvar) ') ∨ mkfs(class, ty, fieldvar) ' .fs .type ≠ void_type ∨ mkfs(class, ty, fieldvar) ' .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(fs ') ∨ mkfs(class, ty, fieldvar) ' .fs ≠ mkfs(fs ' .fs .class, void_type, `initstate' .field))), fs ' ∈ statfields(class0), initdone(class0, st), 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, fs ', st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validstatfield-put-statfield antecedent: succedent: sk ≠ sk0 ∧ ( ¬ is_fskey(sk) ∨ sk .fs .type ≠ void_type ∨ sk .fs ≠ mkfs (`java.lang.Object' .class, void_type, `uninit' .field) ∧ ( ¬ is_fskey(sk0) ∨ sk .fs ≠ mkfs (sk0 .fs .class, void_type, `initstate' .field))) → ( validstatfield(str, sk0, st[jvmref -- sk, val]) ↔ validstatfield(str, sk0, st)) substlist: [val, sk, st, sk0, str] → [val, mkfs(class, ty, fieldvar) ', st, fs ', str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, mkfs(class, ty, fieldvar) ', st, fs ', str)]]