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Proof step 119 from proof validref-refs-last-valid-subset (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 118:
st0[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- _type] = typeval(mkclasstype(class0)), st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), acc + r1 ' = r2 ' + refs, st ⊆ st0, validref(str, r0, mkclasstype(class0), st), class+∃(str, class0), r0 -- _type ∈ st0, r0 ∈ st0, validrefs(str, r2 ' + refs, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, r0 -- mkfs(class, ty0, fieldvar) ' ∈ st0, okval(refval(r2), ty0), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r0, sk, st0), ∀ 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) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), is_abstract(class0), ¬ r2 ∈ acc ∧ r2 ≠ r1, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ validref(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st) ∧ is_reftype(ty0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ goodfieldandtype (r, mkfs(class1, ty, fieldvar) ', st) ↔ r -- mkfs(class1, ty, fieldvar) ' ∈ st ∧ okval (st[ r -- mkfs (class1, ty, fieldvar) '], ty)])]]