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Proof step 15 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty0, is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type) ⊦ r0 = jvmref, r = r0, r = jvmref, ∃ ty1. ty1 ≤ st[r -- _type] .type ∧ 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 14:
st[r -- _type] .type = mkclasstype(class0) ∧ is_classtype(st[r -- _type] .type), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty0, is_reftype(st[r -- _type] .type), type∃(str, st[r -- _type] .type) ⊦ r0 = jvmref, r = r0, r = jvmref, ∃ ty1. ty1 ≤ st[r -- _type] .type ∧ 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] → [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)]]