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Proof step 21 from proof pathex-put-nopathex (previous step)

st[r -- mkfs(class, st[r1 -- _type] .type, fieldvar) '] = refval(r1), is_valid_ref(str, r1, st[r0 -- sk, val]), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st[r0 -- sk, val]), mkfs(class, st[r1 -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0[r3 -- sk0, val0]) → sk0 = _type ∨ path∃(str, r2, r3, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0)) ⊦ st[r1 -- _type] .type = abstract_type, r = r0, r = (r1 ' + refs1) .last, r = jvmref, sk = _type, r1 = jvmref, is_reftype(st[r1 -- _type] .type), path∃(str, r1, r0, st), path∃(str, r1, (r1 ' + refs1) .last, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,¬ is_reftype(st[r -- _type] .type) → ¬ is_valid_ref(str, r, st) ,[st, r, str] → [st[r0 -- sk, val], r1, str] ,F ,addfuns , ,is_valid_ref-reftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])], [EXTRATERMS : (st[r0 -- sk, val], r1, str)]]