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Proof step 112 from proof validref-refs-last-valid-subset (previous step)

validref(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st) ∧ st[st[r0 -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type = st[st[r0 -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type, acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), st[r0 -- _type] = typeval(mkclasstype(class0)), st0[r0 -- _type] = typeval(mkclasstype(class0)), r0 -- mkfs(class, ty0, fieldvar) ' ∈ st0, class0 ≤ class1, mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), validrefs(str, r2 ' + refs, ty0, st0), r0 ∈ st0, r0 -- _type ∈ st0, class+∃(str, class0), validref(str, r0, mkclasstype(class0), st), st ⊆ st0, is_reftype(ty0), validref(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r0, sk, st0) ⊦ r0 = jvmref, is_abstract(class0), validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1, true ∧ st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ∈ acc

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]