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Proof step 60 from proof hassharing-validrefs-dups (previous step)

¬ (is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type), hasSharing(r1, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), validrefs(str, r ' + r1 ' + refs1, st[r -- _type] .type, st), is_valid_ref(str, r, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, hasSharing(r, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
hasSharing(r1, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), validrefs(str, r ' + r1 ' + refs1, st[r -- _type] .type, st), is_array(str, r, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, hasSharing(r, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

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))], [CSIMPSEQ : ⊦ ty ≤ ty])]]