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Proof step 18 from proof validrefkeynotnull-union (previous step)

st[rk] = refval(r), rk ∈ st, st[r -- _type] .type ≤ ty ⊦ r = jvmref, junkref(str, r, st), validref(str, r, ty, st0 ∪ st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ validref(str, r, ty, st) ↔ r = jvmref ∨ st[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st)
Proof step 17:
st[rk] = refval(r), rk ∈ st, st[r -- _type] .type ≤ ty ⊦ r = jvmref, junkref(str, r, st), r = jvmref ∨ (st0 ∪ st)[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st0 ∪ st)

Rule argument

[crewrite-arg: validref-def , F , [st, ty, r, str] → [st0 ∪ st, ty, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0 ∪ st, ty, r, str)]]