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Proof step 16 from proof validrefkeynotnull-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]
Proof step 12:
⊦ ¬ r -- _type ∈ st → (junkref(str, r, st) ↔ r ≠ jvmref)
Proof step 15:
r -- _type ∈ st, st[rk] = refval(r), st[r -- _type] .type ≤ ty, rk ∈ st ⊦ r = jvmref, junkref(str, r, st), st[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st0 ∪ st)

Rule argument

[speclemmaarg: ,rk ∈ st0 → (st ∪ st0)[rk] = st0[rk] ,[rk, st0, st] → [r -- _type, st, st0] ,F ,storefunsx , ,union-at-right-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval])], [EXTRATERMS : (r -- _type, st, st0)]]