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Proof step 44 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)]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 43:
r0 -- _type ≠ r -- mkfs(class, ty0, fieldvar) ', 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)]) ∧ st[r0 -- _type] .type ≤ ty

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r0 -- _type, refval(jvmref), r -- mkfs(class, ty0, fieldvar) ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (r0 -- _type, refval(jvmref), r -- mkfs(class, ty0, fieldvar) ', st)]]