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Proof step 10 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), class0 ≤ class1 ⊦ r = jvmref, r = r0, r0 = jvmref, mkclasstype(class0) ≤ mkclasstype(class0) ∧ type∃(str, mkclasstype(class0)) ∧ ( is_classtype(mkclasstype(class0)) → ¬ interface∃(str, mkclasstype(class0) .class) ∧ (∃ fs. fs ' ∈ instfields(mkclasstype(class0) .class) ∧ st[r0 -- _type] .type ≤ fs .type)) ∧ (is_arraytype(mkclasstype(class0)) → st[r0 -- _type] .type ≤ mkclasstype(class0) .type) ∧ type∃(str, st[r0 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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), class0 ≤ class1, type∃(str, st[r0 -- _type] .type) ⊦ r = jvmref, r = r0, r0 = jvmref, (∃ fs. fs ' ∈ instfields(class0) ∧ st[r0 -- _type] .type ≤ fs .type) ∧ ¬ interface∃(str, class0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ type∃ (str, st[r -- _type] .type) ∧ r ≠ jvmref → ¬ is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_arraytype(mkclasstype(class))], [CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ class ≤ class], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2])]]