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Proof step 63 from proof junkrefs-put-nopathexplus-equiv (previous step)

refs0 .first = st[r -- fs '] .refval, st[r -- _type] .type ≤ ty, junkrefs(str, refs0, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val, sk, r0, st, ty, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, ty, st) → junkrefs(str, r ' + refs, ty, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r, r0, st)) ⊦ refs0 = [], sk = _type, r = jvmref, r = r0, path∃+(str, r, r0, st), junkrefs(str, r ' + refs0, ty, st[r0 -- sk, val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 62:
refs0 = r1 + refs1, r1 = st[r -- fs '] .refval, st[r -- _type] .type ≤ ty, junkrefs(str, refs0, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val, sk, r0, st, ty, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, ty, st) → junkrefs(str, r ' + refs, ty, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r, r0, st)) ⊦ refs0 = [], sk = _type, r = jvmref, r = r0, path∃+(str, r, r0, st), junkrefs(str, r ' + refs0, ty, st[r0 -- sk, val])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r1, refs1] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r1, refs1)]]