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Proof step 8 from proof pathex-subset-equiv (previous step)

st ⊆ st0, validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st0) ⊦ refs0 = [], junkref(str, r, st), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 → (validrefs(str, r ' + refs, ty, st0) ↔ validrefs(str, r ' + refs, ty, st))
Proof step 7:
¬ (validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0), st ⊆ st0, validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st0) ⊦ refs0 = [], junkref(str, r, st), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st)

Rule argument

[crewrite-arg: validrefs-subset-equiv , F , [str, r, st, st0, refs, ty] → [str, r, st, st0, refs0, mkclasstype(`java.lang.Object' .class)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r, st, st0, refs0, mkclasstype(`java.lang.Object' .class))]]