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Proof step 147 from proof validref-refs-last-valid-subset (previous step)

(acc + r1 ') .first = st0[r0 -- fs '] .refval, is_obj(str, r0, st0), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, fs ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- fs ']), validrefs(str, acc + r1 ', fs .type, 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), r ≠ r0 ∧ ¬ r ∈ acc

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 146:
fs = mkfs(class, ty0, fieldvar), (acc + r1 ') .first = st0[r0 -- fs '] .refval, is_obj(str, r0, st0), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, fs ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- fs ']), validrefs(str, acc + r1 ', ty0, 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), r ≠ r0 ∧ ¬ r ∈ acc

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty0, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty0, fieldvar)]]