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Proof step 88 from proof junkrefs-put-refval (previous step)

0 < st[r1 -- _length] .intval, 0 ≤ i, junkrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_referencevalue(st[r1 -- i ']), i < st[r1 -- _length] .intval, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r, st), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, st[r1 -- i '] .refval ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, st[r1 -- i '] .refval ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r0 = jvmref, r1 = jvmref, r = r1, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i '] .refval = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r ≠ st[r1 -- i '] .refval ∧ ¬ r ∈ refs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 87:
st[r1 -- i '] = refval(r2), 0 < st[r1 -- _length] .intval, 0 ≤ i, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_referencevalue(st[r1 -- i ']), i < st[r1 -- _length] .intval, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r, st), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r0 = jvmref, r1 = jvmref, r = r1, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r ≠ r2 ∧ ¬ r ∈ refs

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r1 -- i '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r1 -- i '], r2)]]