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Proof step 27 from proof junkrefs-put-nopathex-equiv (previous step)

acc .first = st[r1 -- fs '] .refval, is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r0, st), fs ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- fs ']), junkrefs(str, acc, fs .type, st), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, acc .first, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, acc, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, acc = [], path∃(str, r1, r0, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
acc = r2 + refs, r2 = st[r1 -- fs '] .refval, is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r0, st), fs ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- fs ']), junkrefs(str, acc, fs .type, st), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, acc, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, acc = [], path∃(str, r1, r0, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc, r2, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc, r2, refs)]]