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Proof step 55 from proof sharing-pathex-field-self (previous step)

st[refs0 .last -- _type] .type = mkclasstype(class), st[refs0 .last -- fs '] = refval(r), # sks = # refs0, st[r -- sks] .refval = refs0 .last, fs ' ∈ instfields(class), validrefs(`docs2store', r ' + refs0, mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), ∀ n. n ≠ 0 ∧ ¬ # refs0 < n → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n] ⊦ refs0 .last = jvmref, refs0 = [], hasSharing(refs0 .last, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 54:
st[r -- sks] = refval(r0) ∧ is_referencevalue(st[r -- sks]), st[refs0 .last -- _type] .type = mkclasstype(class), st[refs0 .last -- fs '] = refval(r), # sks = # refs0, r0 = refs0 .last, fs ' ∈ instfields(class), validrefs(`docs2store', r ' + refs0, mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), ∀ n. n ≠ 0 ∧ ¬ # refs0 < n → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n] ⊦ refs0 .last = jvmref, refs0 = [], hasSharing(refs0 .last, st)

Rule argument

[speclemmaarg: is_referencevalue(val) ,r = val .refval ↔ val = refval(r) ,[val, r] → [st[r -- sks], r0] ,T ,javavalue , ,elim-refval ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r -- sks], r0)]]