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Proof step 6 from proof junkref-addarray-newref (previous step)

newref(r0, st), junkrefs(str, r ' + refs0, (addarray(r0, ty0, vals, st)[r -- _type]) .type, addarray(r0, ty0, vals, st)) ⊦ r0 = jvmref, junkrefs(str, r ' + refs0, st[r -- _type] .type, st), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk]
Proof step 4:
⊦ newref(r, st) → (¬ junkrefs(str, r ' + refs, ty, st) ↔ false)
Proof step 5:
⊦ ¬ junkrefs(str, refs, ty, st) ∧ newref(r0, st) → ¬ junkrefs(str, refs, ty, addarray(r0, ty0, vals, st))

Rule argument

[speclemmaarg: ,rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk] ,[rk, st, vals, ty, r] → [r -- _type, st, vals, ty0, r0] ,F ,addarray , ,add-at-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (r -- _type, st, vals, ty0, r0)]]