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Proof step 42 from proof validstatfields-put-other-statfield (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st))
Proof step 41:
jvmref -- mkfs(class, ty, fieldvar) ' ≠ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∧ jvmref -- mkfs(class, ty, fieldvar) ' ≠ _uninit, 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])

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: init-put-04 antecedent: succedent: rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st)) substlist: [val, rk, st, class] → [val, jvmref -- mkfs(class, ty, fieldvar) ', st, class0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : storekey, , inj-03, ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPNAMEDSEQ : fieldspec, , inj, ⊦ mkfs(class, ty, fieldvar) = mkfs (class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPNAMEDSEQ : specialkeys, , uninit-eq, ⊦ jvmref -- sk = _uninit ↔ sk = mkfs (`java.lang.Object' .class, void_type, `uninit' .field) '])], [EXTRATERMS : (val, jvmref -- mkfs(class, ty, fieldvar) ', st, class0)]]