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Proof step 302 from proof exvalidrefs-maxlength (previous step)

is_obj(str, r, st) ∨ is_array(str, r, st), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r = jvmref, junkref(str, r, st), cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st), validrefs(str, r ', st[r -- _type] .type, st) ∧ ¬ has_reffield(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 301:
is_obj(str, r, st) ∨ is_array(str, r, st), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r = jvmref, junkref(str, r, st), cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st), (r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type) ∧ ¬ has_reffield(r, st)

Rule argument

[crewrite-arg: validrefs-one , F , [st, ty, r, str] → [st, st[r -- _type] .type, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type, r, str)]]