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Proof step 22 from proof validrefs-superclass (previous step)

0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), ∀ ty1, ty2, str0, st0. ty1 ≤ ty2 ∧ validrefs(str0, st[r -- i '] .refval ' + refs, ty1, st0) → validrefs(str0, st[r -- i '] .refval ' + refs, ty2, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i '] .refval = st[r -- i0 '] .refval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
st[r -- i '] = refval(r0), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), ∀ ty1, ty2, str0, st0. ty1 ≤ ty2 ∧ validrefs(str0, r0 ' + refs, ty1, st0) → validrefs(str0, r0 ' + refs, ty2, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval

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)]]