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Proof step 18 from proof addarrays-initdone (previous step)

⊦ mkfs(class, void_type, `initstate' .field) ' = _type, (st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error) ∨ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st) ∧ ( ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(refs, ty, ints, i, st) ∨ (addarrays(refs, ty, ints, i, st)[jvmref -- mkfs(class, void_type, `initstate' .field) ']) ≠ initval(undone)) ∧ (jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(refs, ty, ints, i, st) ∨ ¬ _uninit ∈ addarrays(refs, ty, ints, i, st)) ↔ (¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error)) ∧ ¬ initundone(class, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarrays(refs, ty, ints, i, st) ↔ r -- sk ∈ st)
Proof step 17:
is_fskey(mkfs(class, void_type, `initstate' .field) ') ∧ mkfs(class, void_type, `initstate' .field) ' ≠ _length ∧ mkfs(class, void_type, `initstate' .field) ' ≠ _type ⊦ mkfs(class, void_type, `initstate' .field) ' = _type, (st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error) ∨ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st) ∧ ( ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ (addarrays(refs, ty, ints, i, st)[jvmref -- mkfs(class, void_type, `initstate' .field) ']) ≠ initval(undone)) ∧ (jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ ¬ _uninit ∈ addarrays(refs, ty, ints, i, st)) ↔ (¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error)) ∧ ¬ initundone(class, st)

Rule argument

[crewrite-arg: addarrays-fieldin , F , [st, i, ints, ty, refs, sk, r] → [st, i, ints, ty, refs, mkfs(class, void_type, `initstate' .field) ', jvmref] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ mkfs (class1, ty, `initstate' .field) ' ≠ _length])], [EXTRATERMS : (st, i, ints, ty, refs, mkfs(class, void_type, `initstate' .field) ', jvmref)]]