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Proof step 18 from proof unchNorec-validrefs (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r -- _type] = st0[r -- _type], is_obj(str, r, st0), is_obj(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, r1 ' + refs, ty0, st), ∀ 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), ∀ r0. r0 = r1 ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ r1 = st0[r -- fs '] .refval ∧ validrefs(str, r1 ' + refs, fs .type, st0)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- mkfs(class, ty0, fieldvar) '], r1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) '], r1)]]