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Proof step 13 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), st[r0 -- _type] .type ≤ ty0, is_valid_ref(str, r0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), is_classtype(ty), class0 ≤ ty .class ⊦ r = jvmref, r = r0, r0 = jvmref, ∃ ty1. ty1 ≤ mkclasstype(class0) ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r0 -- _type] .type ≤ ty1 .type) ∧ type∃(str, st[r0 -- _type] .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
ty = mkclasstype(class1), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), st[r0 -- _type] .type ≤ ty0, is_valid_ref(str, r0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), is_classtype(ty), class0 ≤ class1 ⊦ r = jvmref, r = r0, r0 = jvmref, ∃ ty1. ty1 ≤ mkclasstype(class0) ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty1) → st[r0 -- _type] .type ≤ ty1 .type) ∧ type∃(str, st[r0 -- _type] .type)

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [ty, class1] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (ty, class1)]]