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Proof step 87 from proof validrefs-not-contains (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), st[r -- _type] .type = mkclasstype(class0), is_obj(str, r, st), tdname+∃(str, class0), contains(str, st[r0 -- _type] .type ' + tys + st[r1 -- _type] .type '), validrefs(str, r0 ' + refs0 + r1 ', ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(class0), is_classtype(ty), class0 ≤ ty .class ⊦ r = jvmref, r = r1, r1 = jvmref, r0 = r1, ∃ ty0. ty0 ≤ mkclasstype(class0) ∧ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ is_classtype(ty) → is_reftype(ty)])]]