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Proof step 17 from proof validrefkeynotnull-subset (previous step)

rk ∈ st ∧ st ⊆ st1, st[rk] = refval(r), rk ∈ st, st ⊆ st1, rk ∈ st1, st[r -- _type] .type ≤ ty ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st[rk]) ∧ st[rk] .refval ≠ jvmref ∧ st1[st[rk] .refval -- _type] .type ≤ ty ∧ ¬ junkref(str, st[rk] .refval, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 13:
⊦ ¬ r -- _type ∈ st → (junkref(str, r, st) ↔ r ≠ jvmref)
Proof step 16:
st[rk] .refval -- _type ∈ st ∧ st ⊆ st1, rk ∈ st ∧ st ⊆ st1, st[rk] = refval(r), rk ∈ st, st ⊆ st1, rk ∈ st1, st[r -- _type] .type ≤ ty ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st[rk]) ∧ st[rk] .refval ≠ jvmref ∧ st[st[rk] .refval -- _type] .type ≤ ty ∧ ¬ junkref(str, st[rk] .refval, st1)

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [st[rk] .refval -- _type, st, st1] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval])], [EXTRATERMS : (st[rk] .refval -- _type, st, st1)]]