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Proof step 38 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), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 37:
¬ ( (r ' + refs) .last ≠ jvmref ∧ (¬ is_valid_ref(str, (r ' + refs) .last, st) ∨ ¬ st[(r ' + refs) .last -- _type] .type ≤ st[(r ' + refs) .last -- _type] .type)), 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), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, st[(r ' + refs) .last -- _type] .type, r0 ', (r ' + refs) .last, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[(r ' + refs) .last -- _type] .type, r0 ', (r ' + refs) .last, str)]]