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Proof step 10 from proof validsubset-trans (previous step)

r0 ∈ st0, r0 ∈ st1, junkref(str, r0, st1), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1) ⊦ r0 ∈ st, junkref(str, r0, st0), validref(str, r0, st0[r0 -- _type] .type, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ validref(str, r, st[r -- _type] .type, st) ↔ ¬ junkref(str, r, st)

Rule argument

[crewrite-arg: validref-runtimetype, F, [st, r, str] → [st0, r0, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, r0, str)]]