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Proof step 4 from proof addarrays-mode-01 (previous step)

⊦ jvmref -- mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ addarrays(refs, ty, ints, i, st) ↔ jvmref -- mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarrays(refs, ty, ints, i, st) ↔ r -- sk ∈ st)
Proof step 3:
⊦ rk ∈ st → rk ∈ addarrays(refs, ty, ints, i, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ jvmref -- mkfs (`java.lang.Object' .class, void_type, `mode' .field) ' = _mode], [CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPFORWARD : ⊦ mkfs(class1, ty, fieldvar) ' = _length → class1 = `*Array*' .class ∧ ty = int_type ∧ fieldvar = `length' .field], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0], [CSIMPFORWARD : ⊦ _type = mkfs(class1, ty, fieldvar) ' → class1 = `java.lang.Object' .class ∧ ty = void_type ∧ fieldvar = `type' .field])], [EXTRATERMS : (st, i, ints, ty, refs, mkfs (`java.lang.Object' .class, void_type, `mode' .field) ', jvmref)]]