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Proof step 41 from proof unchNorec-junkrefs (previous step)

st[r -- _type] = st0[r -- _type], st[r -- i '] = refval(r1), st[r -- _length] = st0[r -- _length], st0[r -- _type] .type = mkarraytype(ty1), junkrefs(str, r1 ' + refs, ty1, st), i < st0[r -- _length] .intval, is_array(str, r, st0), is_array(str, r, st), 0 ≤ i, unchangedNorec(r, st, st0), mkarraytype(ty1) ≤ ty, 0 < st0[r -- _length] .intval, ∀ str0, ty0, st1, st2. junkrefs(str0, r1 ' + refs, ty0, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → junkrefs(str0, r1 ' + refs, ty0, st2), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, is_referencevalue(st0[r -- i ']) ∧ r1 = st0[r -- i '] .refval ∧ junkrefs(str, st0[r -- i '] .refval ' + refs, ty1, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchNorec-index0 antecedent: succedent: unchangedNorec(r, st, st0) ∧ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_arraytype(st0[r -- _type] .type) ∧ r ≠ jvmref → st0[r -- i '] = st[r -- i '] substlist: [r, st, st0, i] → [r, st, st0, i] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)])], [EXTRATERMS : (r, st, st0, i)]]