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Proof step 40 from proof pathexplus-pathex (previous step)

validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, refs + refs0, ty, st)
Proof step 39:
¬ validrefs(str, (r ' + refs) .last ' + r0 ', st[((r ' + refs) .last ' + r0 ') .first -- _type] .type, st) ∧ (r ' + refs) .last ' + r0 ' ≠ [] → ¬ validrefs(str, (r ' + refs) .butlast + (r ' + refs) .last ' + r0 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

Rule argument

[LEMMAARG : validrefs-postfix, [str, refs0, st, refs, ty] → [str, (r ' + refs) .last ' + r0 ', st, (r ' + refs) .butlast, mkclasstype(`java.lang.Object' .class)]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, (r ' + refs) .last ' + r0 ', st, (r ' + refs) .butlast, mkclasstype(`java.lang.Object' .class))]]