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Proof step 9 from proof cyclic-addobj-other-01 (previous step)

newref(r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs0, st[r -- _type] .type, addobj(r0, class, fis, st)), r = r0, r0 = jvmref, junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ validrefs(str, refs, ty, st) ∧ ¬ r ∈ refs → validrefs(str, refs, ty, addobj(r, class, fis, st))
Proof step 8:
¬ (validrefs(str, r ' + refs0, st[r -- _type] .type, st) ∧ ¬ r0 ∈ r ' + refs0), newref(r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs0, st[r -- _type] .type, addobj(r0, class, fis, st)), r = r0, r0 = jvmref, junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[crewrite-arg: validrefs-addobj-notin , F , [st, fis, class, r, ty, refs, str] → [st, fis, class, r0, st[r -- _type] .type, r ' + refs0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis, class, r0, st[r -- _type] .type, r ' + refs0, str)]]