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Proof step 52 from proof unchanged-junkrefs-level (previous step)

st1[r -- _type] = st[r -- _type], unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), is_obj(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), junkrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ str1, st0, st2, str2, ty0. unchanged(str1, st[r -- mkfs(class, ty1, fieldvar) '] .refval, st0, st2) ∧ junkrefs(str2, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty0, st0) ∧ level⊆(str2, str1) → junkrefs(str2, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty0, st2) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ st[r -- mkfs(class, ty1, fieldvar) '] .refval = st1[r -- fs0 '] .refval ∧ junkrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs0 .type, st1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), st1[r -- _type] = st[r -- _type], unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), is_obj(str, r, st), is_obj(str, r, st1), is_valid_ref(str0, r, st1), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), junkrefs(str, r1 ' + refs, ty1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ str1, st0, st2, str2, ty0. unchanged(str1, r1, st0, st2) ∧ junkrefs(str2, r1 ' + refs, ty0, st0) ∧ level⊆(str2, str1) → junkrefs(str2, r1 ' + refs, ty0, st2) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ r1 = st1[r -- fs0 '] .refval ∧ junkrefs(str, r1 ' + refs, fs0 .type, st1)

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, ty1, 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, ty1, fieldvar) '], r1)]]