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Proof step 17 from proof unchNorec-transitivity (previous step)

st[r -- _type] = st1[r -- _type], st0[r -- _type] = st1[r -- _type], unchangedNorec(r, st, st0), unchangedNorec(r, st0, st1), is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st0[r -- i0 ']), is_classtype(st1[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r -- _type] .type .class) → st[r -- fs '] = st0[r -- fs ']) ⊦ r = jvmref, (is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st1[r -- _length] ∧ (0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st1[r -- i '])) ∧ (is_classtype(st1[r -- _type] .type) → (fs ' ∈ instfields(st1[r -- _type] .type .class) → st[r -- fs '] = st1[r -- fs ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ ( st[r -- _type] = st0[r -- _type] ∧ (is_classtype(st[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) → st[r -- fs '] = st0[r -- fs '])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st0[r -- i ']))) ∧ r ≠ jvmref → ¬ unchangedNorec(r, st, st0)
Proof step 16:
¬ ( ¬ ( st0[r -- _type] = st1[r -- _type] ∧ (is_classtype(st0[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) → st0[r -- fs '] = st1[r -- fs '])) ∧ ( is_arraytype(st0[r -- _type] .type) → st0[r -- _length] = st1[r -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st0[r -- _length] .intval → st0[r -- i '] = st1[r -- i ']))) ∧ r ≠ jvmref), st[r -- _type] = st1[r -- _type], st0[r -- _type] = st1[r -- _type], unchangedNorec(r, st, st0), unchangedNorec(r, st0, st1), is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st0[r -- i0 ']), is_classtype(st1[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r -- _type] .type .class) → st[r -- fs '] = st0[r -- fs ']) ⊦ r = jvmref, (is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st1[r -- _length] ∧ (0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st1[r -- i '])) ∧ (is_classtype(st1[r -- _type] .type) → (fs ' ∈ instfields(st1[r -- _type] .type .class) → st[r -- fs '] = st1[r -- fs ']))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchNorec-def-keep antecedent: succedent: ¬ ( st[r -- _type] = st0[r -- _type] ∧ ( is_classtype(st[r -- _type] .type) → (∀ sk. sk ∈ instfields(st[r -- _type] .type .class) → st[r -- sk] = st0[r -- sk])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st0[r -- i ']))) ∧ r ≠ jvmref → ¬ unchangedNorec(r, st, st0) substlist: [st0, st, r] → [st1, st0, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, st0, r)]]