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Proof step 9 from proof validref-nopath-superset (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 8:
r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st0) ∧ st0[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), validrefnotnull(str, r, st[r -- _type] .type, st), st ⊆ st0, newref(r, st) ⊦ r = jvmref

Rule argument

[crewrite-arg: validrefs-one , F , [st, ty, r, str] → [st0, mkclasstype(`java.lang.Object' .class), r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, mkclasstype(`java.lang.Object' .class), r, str)]]