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Proof step 8 from proof cyclic-subset-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 4:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 7:
r -- _type ∈ st ∧ st ⊆ st0, st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs0, st[r -- _type] .type, st0), junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [r -- _type, st, st0] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ r -- _type ∈ st → ( junkref(str, r, st) ↔ r ≠ jvmref)])], [EXTRATERMS : (r -- _type, st, st0)]]