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Proof step 48 from proof validrefs-put-notin-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: At-other antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] substlist: [rk, val, rk0, st] → [r -- i ', val, r -- sk, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : specialkeys, , len, ⊦ _length ≠ i '], [CSIMPNAMEDSEQ : specialkeys, , type-03, ⊦ _type ≠ i '], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (r -- i ', val, r -- sk, st)]]