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Proof step 9 from proof cyclic-subset (previous step)

st ⊆ st0, validrefs(str, r ' + refs0, st0[r -- _type] .type, st0) ⊦ st0[r -- _type] = st[r -- _type], validrefs(str, r ' + refs0, st[r -- _type] .type, st), junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 8:
∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk], validrefs(str, r ' + refs0, st0[r -- _type] .type, st0) ⊦ st0[r -- _type] = st[r -- _type], validrefs(str, r ' + refs0, st[r -- _type] .type, st), junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st0, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st)]]