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Proof step 88 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs0 + r1 ', ty1, st), contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type '), is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type) ⊦ r0 = r1, r1 = jvmref, r = r1, r = jvmref, ∃ ty0. ty0 ≤ st[r -- _type] .type ∧ type∃(str, ty0) ∧ (is_classtype(ty0) → ¬ interface∃(str, ty0 .class) ∧ (∃ fs. fs ' ∈ instfields(ty0 .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty0) → st[r0 -- _type] .type ≤ ty0 .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 87:
st[r -- _type] .type = mkclasstype(class0) ∧ is_classtype(st[r -- _type] .type), st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), validrefs(str, r0 ' + refs0 + r1 ', ty1, st), contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type '), is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type) ⊦ r0 = r1, r1 = jvmref, r = r1, r = jvmref, ∃ ty0. ty0 ≤ st[r -- _type] .type ∧ type∃(str, ty0) ∧ (is_classtype(ty0) → ¬ interface∃(str, ty0 .class) ∧ (∃ fs. fs ' ∈ instfields(ty0 .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(ty0) → st[r0 -- _type] .type ≤ ty0 .type)

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r -- _type] .type, class0] ,T ,javatype , ,elim-02 ]

Additional information

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