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Proof step 8 from proof cyclic-delete (previous step)

validrefs(str, r ' + refs0, (st -- r0)[r -- _type] .type, st -- r0) ⊦ ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]
Proof step 4:
⊦ validrefs(str, r ' + refs, ty, st -- r) ↔ r = jvmref ∧ refs = []
Proof step 7:
r0 ≠ r, validrefs(str, r ' + refs0, st[r -- _type] .type, st -- r0) ⊦ ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Rule argument

[speclemmaarg: ,r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0] ,[sk0, r0, r, st] → [_type, r, r0, st] ,F ,storefuns , ,look-del ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ dups([])])], [EXTRATERMS : (_type, r, r0, st)]]