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Proof step 48 from proof validstatfields-put-other-statfield (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 26:
∀ class0, sk. tdname∃(str, class0) ∧ initdone(class0, st[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ sk ∈ statfields(class0) → validstatfield(str, sk, st[jvmref -- mkfs(class, ty, fieldvar) ', val]) ⊦ ∀ class, sk. tdname∃(str, class) ∧ initdone(class, st) ∧ sk ∈ statfields(class) → validstatfield(str, sk, st), class = `java.lang.Object' .class, tdname∃(str, class)
Proof step 47:
∀ class, sk. tdname∃(str, class) ∧ initdone(class, st) ∧ sk ∈ statfields(class) → validstatfield(str, sk, st) ⊦ ∀ class0, sk. tdname∃(str, class0) ∧ initdone(class0, st[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ sk ∈ statfields(class0) → validstatfield(str, sk, st[jvmref -- mkfs(class, ty, fieldvar) ', val]), class = `java.lang.Object' .class, tdname∃(str, class)

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]