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Proof step 37 from proof validstatfields-put-statfield-06 (previous step)

⊦ statfields(class) = [] ∨ tdname∃(str, class) ↔ validstatfields(str, statfields(class), st), class0 = class, initdone(class, st[jvmref -- mkfs(class0, void_type, `initstate' .field) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st))
Proof step 36:
⊦ ¬ initdone(class, st) → (validstatfields(str, statfields(class), st) ↔ statfields(class) = [] ∨ tdname∃(str, class))

Rule argument

[speclemmaarg: , rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st)) ,[val, rk, st, class] → [val, jvmref -- mkfs(class0, void_type, `initstate' .field) ', st, class] ,F ,storefuns , ,init-put-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ jvmref -- sk = _uninit ↔ sk = mkfs (`java.lang.Object' .class, void_type, `uninit' .field) '], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0])], [EXTRATERMS : (val, jvmref -- mkfs(class0, void_type, `initstate' .field) ', st, class)]]