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Proof step 139 from proof validrefs-not-contains (previous step)

0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs0 + r1 ', st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[st[r -- i '] .refval -- _type] .type, st0[r1 -- _type] .type) ∧ st[r -- i '] .refval ≠ r1 → ¬ validrefs(str0, st[r -- i '] .refval ' + refs0 + r1 ', ty0, st0) ⊦ r = jvmref, r = r1, r1 = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 138:
st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0 + r1 ', st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[r0 -- _type] .type, st0[r1 -- _type] .type) ∧ r0 ≠ r1 → ¬ validrefs(str0, r0 ' + refs0 + r1 ', ty0, st0) ⊦ r = jvmref, r = r1, r1 = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- i '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i '], r0)]]