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Proof step 14 from proof unchNorec-validrefs (previous step)

st[r -- _type] = st0[r -- _type], st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), unchangedNorec(r, st, st0), st0[r -- _type] .type ≤ ty, is_obj(str, r, st), is_obj(str, r, st0), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2) ⊦ r = jvmref, is_referencevalue(st0[r -- mkfs(class, ty0, fieldvar) ']) ∧ r1 = st0[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, st0[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ unchangedNorec(r, st, st0) ∧ fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_classtype(st0[r -- _type] .type) ∧ r ≠ jvmref → st0[r -- fs '] = st[r -- fs ']
Proof step 13:
unchangedNorec(r, st, st0) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_classtype(st0[r -- _type] .type) ∧ r ≠ jvmref, st[r -- _type] = st0[r -- _type], st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), unchangedNorec(r, st, st0), st0[r -- _type] .type ≤ ty, is_obj(str, r, st), is_obj(str, r, st0), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0), ∀ str0, ty1, st1, st2. validrefs(str0, r1 ' + refs, ty1, st1) ∧ (∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, r1 ' + refs, ty1, st2) ⊦ r = jvmref, is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ r1 = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchNorec-field0 antecedent: succedent: unchangedNorec(r, st, st0) ∧ fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_classtype(st0[r -- _type] .type) ∧ r ≠ jvmref → st0[r -- fs '] = st[r -- fs '] substlist: [r, st, st0, fs] → [r, st, st0, mkfs(class, ty0, fieldvar)] 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 : ⊦ ¬ is_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (r, st, st0, mkfs(class, ty0, fieldvar))]]