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Proof step 46 from proof unchanged-junkrefs-level (previous step)

st1[r -- _type] = st[r -- _type], st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), junkrefs(str, r1 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_valid_ref(str0, r, st1), is_obj(str, r, st1), is_obj(str, r, st), unchangedNorec(r, st, st1), is_valid_ref(str0, r, st), level⊆(str, str0), unchanged(str0, r, st, st1), is_classtype(st[r -- _type] .type), ∀ 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), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) → st[r -- fs '] = st1[r -- fs '] ⊦ r = jvmref, is_referencevalue(st1[r -- mkfs(class, ty1, fieldvar) ']) ∧ r1 = st1[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ junkrefs(str, st1[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
st[r -- _type] .type = mkclasstype(class0), st1[r -- _type] = st[r -- _type], st[r -- mkfs(class, ty1, fieldvar) '] = refval(r1), junkrefs(str, r1 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, is_valid_ref(str0, r, st1), is_obj(str, r, st1), is_obj(str, r, st), unchangedNorec(r, st, st1), is_valid_ref(str0, r, st), level⊆(str, str0), unchanged(str0, r, st, st1), is_classtype(st[r -- _type] .type), ∀ 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), ∀ 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 '] ⊦ r = jvmref, is_referencevalue(st1[r -- mkfs(class, ty1, fieldvar) ']) ∧ r1 = st1[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ junkrefs(str, st1[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st1)

Rule argument

[x0lemmaarg: spec-name: javatype instance-name: lemma-name: elim-02 antecedent: succedent: is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) substlist: [ty, class] → [st[r -- _type] .type, class0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r -- _type] .type, class0)]]