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Proof step 16 from proof unchanged-junkrefs-level (previous step)

st1[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), st1[r -- _type] = st[r -- _type], st[r -- _type] .type = mkclasstype(class0), st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), path∃(str0, r, r1, st1), mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), junkrefs(str, r1 ' + refs, ty1, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_obj(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), is_obj(str, r, st1), is_valid_ref(str0, r, st1), class0 ≤ class1, path∃(str0, r, r1, st), unchangedNorec(r1, st, st1), is_valid_ref(str0, r1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ fs. fs ' ∈ instfields(class0) → st[r -- fs '] = st1[r -- fs '] ⊦ r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), st[r1 -- _type] .type ≤ ty1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ ( 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 15:
¬ ( ¬ ( st[r1 -- _type] = st1[r1 -- _type] ∧ (is_classtype(st[r1 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) → st[r1 -- fs '] = st1[r1 -- fs '])) ∧ ( is_arraytype(st[r1 -- _type] .type) → st[r1 -- _length] = st1[r1 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval → st[r1 -- i '] = st1[r1 -- i ']))) ∧ r1 ≠ jvmref), st1[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), st1[r -- _type] = st[r -- _type], st[r -- _type] .type = mkclasstype(class0), st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), path∃(str0, r, r1, st1), mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), junkrefs(str, r1 ' + refs, ty1, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_obj(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), is_obj(str, r, st1), is_valid_ref(str0, r, st1), class0 ≤ class1, path∃(str0, r, r1, st), unchangedNorec(r1, st, st1), is_valid_ref(str0, r1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ fs. fs ' ∈ instfields(class0) → st[r -- fs '] = st1[r -- fs '] ⊦ r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), st[r1 -- _type] .type ≤ ty1

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) → (∀ 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) substlist: [st0, st, r] → [st1, st, r1] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 16)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, st, r1)]]