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Proof step 12 from proof validref-nopath-superset (previous step)

validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st0), validrefnotnull(str, r, st[r -- _type] .type, st), st ⊆ st0, newref(refs0 .last, st) ⊦ refs0 = [], r = jvmref, refs0 .last = jvmref

User applied rule insert lemma

And obtained the following new goals

Proof step 11:
⊦ r ∈ refs0 ∧ validrefs(str, refs0 + r1, ty, st0) ∧ validrefnotnull(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 → ¬ newref(r1, st)

Rule argument

[LEMMAARG : validrefs-subset-notnew, [r, refs0, str, r1, ty, st0, st] → [r, r ' + refs0 .butlast, str, refs0 .last, mkclasstype(`java.lang.Object' .class), st0, st]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r = refs + r '], [CSIMPSEQ : refs ≠ [] ⊦ refs .butlast + refs .last ' = refs])], [EXTRATERMS : (r, r ' + refs0 .butlast, str, refs0 .last, mkclasstype(`java.lang.Object' .class), st0, st)]]