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Proof step 50 from proof junkrefs-put-null (previous step)

acc .first = st[r0 -- i '] .refval, junkrefs (str, acc, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, ∀ str, ty, st, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ is_obj(r, st) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, acc = [], junkrefs(str, r0 ' + acc, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 49:
acc = r1 + refs, r1 = st[r0 -- i '] .refval, junkrefs (str, acc, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, ∀ str, ty, st, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ is_obj(r, st) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, acc = [], junkrefs(str, r0 ' + acc, ty, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc, r1, 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, r1, refs)]]