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Proof step 7 from proof junkref-addobj (previous step)

newref(r0, st), junkrefs(str, r ' + refs0, (addobj(r0, class, fis, st)[r -- _type]) .type, addobj(r0, class, fis, st)), junkrefs(str, r ' + refs0, (addobj(r0, class, fis, st)[r -- _type]) .type, st) ⊦ r0 = jvmref, junkrefs(str, r ' + refs0, st[r -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 5:
⊦ newref(r, st) → (¬ junkrefs(str, r ' + refs, ty, st) ↔ false)
Proof step 6:
⊦ ¬ junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → (junkrefs(str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty)

Rule argument

[speclemmaarg: ,r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk] ,[sk, r0, st, fis, class1, r] → [_type, r, st, fis, class, r0] ,F ,addfuns , ,add-ref ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ sk ∈ fis → (addobj(r, class, fis, st) [r -- sk ] ) = fis[sk]], [CSIMPSEQ : ¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st) [r -- _type ] ) = typeval(mkclasstype(class1))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty])], [EXTRATERMS : (_type, r, st, fis, class, r0)]]