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Proof step 5 from proof validrefs-superset-junkref (previous step)

validrefs(str, r ' + refs, ty, st0), r0 ∈ refs, newref(r0, st), st ⊆ st0 ⊦ r0 = jvmref, junkref(str, r, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ validrefs(str, refs, ty, st0) ∧ st ⊆ st0 ∧ ¬ junkref(str, r, st) ∧ refs ≠ [] ∧ refs .first = r → validrefs(str, refs, ty, st)
Proof step 4:
validrefs(str, r ' + refs, ty, st0) ∧ st ⊆ st0 ∧ ¬ junkref(str, r, st) ∧ r ' + refs ≠ [] ∧ (r ' + refs) .first = r → validrefs(str, r ' + refs, ty, st), validrefs(str, r ' + refs, ty, st0), r0 ∈ refs, newref(r0, st), st ⊆ st0 ⊦ r0 = jvmref, junkref(str, r, st)

Rule argument

[LEMMAARG : validrefs-subset, [str, refs, ty, st0, st, r] → [str, r ' + refs, ty, st0, st, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r ' + refs, ty, st0, st, r)]]