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Proof step 42 from proof junkrefs-put-null-01 (previous step)

st[r0 -- _type] .type ≤ ty, is_reftype(ty0), junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_array(str, r0, st), ∀ str, ty, st, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ is_reftype(fs .type) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st), is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ r ≠ r0 → (is_array(str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))
Proof step 41:
¬ r ≠ r0, st[r0 -- _type] .type ≤ ty, is_reftype(ty0), junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_array(str, r0, st), ∀ str, ty, st, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ is_reftype(fs .type) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st), is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)])

Rule argument

[speclemmaarg: , r ≠ r0 → (is_array(str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st)) ,[val, sk, r, st, r0, str] → [refval(jvmref), mkfs(class, ty0, fieldvar) ', r, st, r0, str] ,F ,okfuns , ,is_array-put-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(jvmref), mkfs(class, ty0, fieldvar) ', r, st, r0, str)]]