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Proof step 35 from proof initsubset-put-statfield (previous step)

sk .fs = mkfs(class, ty, fieldvar), validstatfield(str, sk, st0[jvmref -- sk, val]), init⊆(str, st, st0), is_fskey(sk), fieldvar ≠ `initstate' .field ∧ sk ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ' ∨ ty ≠ void_type ⊦ (∀ class. initdone(class, st) → initdone(class, st0[jvmref -- sk, val])) ∧ (∀ class. initerror(class, st) → initerror(class, st0[jvmref -- sk, val])) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st0[jvmref -- sk, val]) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0[jvmref -- sk, val])) ∧ (∀ class, sk0. initdone(class, st) ∧ initdone(class, st0[jvmref -- sk, val]) ∧ tdname∃(str, class) ∧ sk0 ∈ statfields(class) ∧ validstatfield(str, sk0, st) → validstatfield(str, sk0, st0[jvmref -- sk, val]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ init⊆(str, st, st0) ↔ (∀ class. initdone(class, st) → initdone(class, st0)) ∧ (∀ class. initerror(class, st) → initerror(class, st0)) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0)) ∧ (∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0))
Proof step 34:
sk .fs = mkfs(class, ty, fieldvar), validstatfield(str, sk, st0[jvmref -- sk, val]), (∀ class. initdone(class, st) → initdone(class, st0)) ∧ (∀ class. initerror(class, st) → initerror(class, st0)) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0)) ∧ (∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0)), is_fskey(sk), fieldvar ≠ `initstate' .field ∧ sk ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ' ∨ ty ≠ void_type ⊦ (∀ class. initdone(class, st) → initdone(class, st0[jvmref -- sk, val])) ∧ (∀ class. initerror(class, st) → initerror(class, st0[jvmref -- sk, val])) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st0[jvmref -- sk, val]) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0[jvmref -- sk, val])) ∧ (∀ class, sk0. initdone(class, st) ∧ initdone(class, st0[jvmref -- sk, val]) ∧ tdname∃(str, class) ∧ sk0 ∈ statfields(class) ∧ validstatfield(str, sk0, st) → validstatfield(str, sk0, st0[jvmref -- sk, val]))

Rule argument

[crewrite-arg: initsubset-def, F, [st0, st, str] → [st0, st, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st, str)]]