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Proof step 21 from proof unchanged-rec-generic (previous step)

st[r -- sk] = refval(r0), sk .fs = mkfs(class, ty, fieldvar), st[r -- _type] .type = mkarraytype(ty0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ sk .index, sk .index < st[r -- _length] .intval, is_indexkey(sk), unchanged(str, r, st, st0), is_referencevalue(st[r -- sk .index ']) ∧ ( st[r -- sk .index '] .refval ≠ jvmref → st[st[r -- sk .index '] .refval -- _type] .type ≤ ty0 ∧ is_valid_ref(str, st[r -- sk .index '] .refval, st)) → unchanged(str, st[r -- sk .index '] .refval, st, st0) ⊦ r = jvmref, unchanged(str, r0, st, st0), junkref(str, r, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
sk = i ', st[r -- sk] = refval(r0), sk .fs = mkfs(class, ty, fieldvar), st[r -- _type] .type = mkarraytype(ty0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_indexkey(sk), unchanged(str, r, st, st0), is_referencevalue(st[r -- i ']) ∧ (st[r -- i '] .refval ≠ jvmref → st[st[r -- i '] .refval -- _type] .type ≤ ty0 ∧ is_valid_ref(str, st[r -- i '] .refval, st)) → unchanged(str, st[r -- i '] .refval, st, st0) ⊦ r = jvmref, unchanged(str, r0, st, st0), junkref(str, r, st)

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: elim-04 antecedent: succedent: is_indexkey(sk) → (i = sk .index ↔ sk = i ') substlist: [sk, i] → [sk, i] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i)]]