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Proof step 28 from proof validrefs-all-same (previous step)

st0[r -- _type] = typeval(mkclasstype(class0)), st[r -- _type] = typeval(mkclasstype(class0)), r ∈ st, r ∈ st0, r -- _type ∈ st0, class0 ≤ class1, goodfieldsandtypes(r, instfields(class0), st), r -- _type ∈ st, class+∃(str, class0), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk], refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(class0) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])) ⊦ r = jvmref, validrefs(str, r ' + refs0, mkclasstype(class1), st0), is_abstract(class0), goodfieldsandtypes(r, instfields(class0), st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st))
Proof step 27:
st0[r -- _type] = typeval(mkclasstype(class0)), st[r -- _type] = typeval(mkclasstype(class0)), r ∈ st, r ∈ st0, r -- _type ∈ st0, class0 ≤ class1, goodfieldsandtypes(r, instfields(class0), st), r -- _type ∈ st, class+∃(str, class0), ∀ sk. sk ∈ instfields(class0) → st[r -- sk] = st0[r -- sk], refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(class0) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, refs0, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, refs0, ty0, st1) ∧ (∀ r0. r0 ∈ refs0 ∧ r0 ≠ jvmref → st1[r0 -- _type] = st2[r0 -- _type] ∧ (is_classtype(st1[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st1[r0 -- _type] .type .class) → st1[r0 -- sk] = st2[r0 -- sk])) ∧ ( is_arraytype(st1[r0 -- _type] .type) → st1[r0 -- _length] = st2[r0 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st1[r0 -- _length] .intval → st1[r0 -- i '] = st2[r0 -- i ']))) → validrefs(str0, refs0, ty0, st2), ∀ r0. (r0 = r ∨ r0 ∈ refs0) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])) ⊦ r = jvmref, validrefs(str, r ' + refs0, mkclasstype(class1), st0), is_abstract(class0), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st0)

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: gfts-all antecedent: succedent: goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)) substlist: [st, sks, r] → [st0, instfields(class0), r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, instfields(class0), r)]]