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Proof step 14 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), st[r1 -- _type] = st1[r1 -- _type], 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 '], is_classtype(st1[r1 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r1 -- _type] .type .class) → st[r1 -- fs '] = st1[r1 -- fs ']), is_arraytype(st1[r1 -- _type] .type) → st[r1 -- _length] = st1[r1 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i → st[r1 -- i '] = st1[r1 -- i ']) ⊦ r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), st1[r1 -- _type] .type ≤ ty1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: junkrefs-is-junk antecedent: succedent: r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st) substlist: [st, ty, refs, r, str] → [st1, ty1, refs, r1, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st1, ty1, refs, r1, str)]]