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Proof step 85 from proof validref-refs-last-valid-subset (previous step)

¬ (is_obj(str, r0, st0) ∧ st0[r0 -- _type] .type ≤ ty), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, validrefs(str, (r0 ' + acc) + r1 ', ty, st0), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
st0[r0 -- _type] .type ≤ ty, validref(str, r, st[r -- _type] .type, st), st ⊆ st0, validrefs(str, (r0 ' + acc) + r1 ', ty, st0), is_array(str, 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, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))])]]