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Proof step 52 from proof validrefs-put-notin-03 (previous step)

i < st[r -- _length] .intval, is_referencevalue(st[r -- sk, val][r -- i ']), validrefs(str, (st[r -- sk, val][r -- i ']) .refval ' + refs1, st[r -- _type] .type .type, st[r -- sk, val]), is_array(str, r, st), is_valid_ref(r, st), is_array(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ sk = _length, sk = _type, (st[r -- sk, val][r -- i ']) .refval = st[r -- sk] .refval, val .refval = (st[r -- sk, val][r -- i ']) .refval, r = (st[r -- sk, val][r -- i ']) .refval, r = jvmref, (st[r -- sk, val][r -- i ']) .refval ∈ refs1, dups(refs1), r ∈ refs1, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ (st[r -- sk, val][r -- i ']) .refval = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i0 '] .refval ' + refs1, st[r -- _type] .type .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
(st[r -- sk, val][r -- i ']) = refval(r0), i < st[r -- _length] .intval, is_referencevalue(st[r -- sk, val][r -- i ']), validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r -- sk, val]), is_array(str, r, st), is_valid_ref(r, st), is_array(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, r0 ∈ refs1, dups(refs1), r ∈ refs1, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i0 '] .refval ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- sk, val][r -- i '], r0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

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