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Proof step 129 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- _type] = typeval(mkclasstype(st0[r0 -- _type] .type .class)), r0 -- _type ∈ st0, is_typevalue(st0[r0 -- _type]), is_classtype(st0[r0 -- _type] .type), is_obj(r0, st0[r0 -- _type] .type .class, st0), class+∃(str, st0[r0 -- _type] .type .class), validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty0, st0), r0 ∈ 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, is_abstract(st0[r0 -- _type] .type .class), validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 128:
st0[r0 -- _type] .type = mkclasstype(class0), acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- _type] = typeval(mkclasstype(class0)), r0 -- _type ∈ st0, is_typevalue(st0[r0 -- _type]), is_classtype(st0[r0 -- _type] .type), is_obj(r0, class0, st0), class+∃(str, class0), validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), validrefs(str, r2 ' + refs, ty0, st0), r0 ∈ 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, is_abstract(class0), validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st0[r0 -- _type] .type, class0] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st0[r0 -- _type] .type, class0)]]