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Proof step 59 from proof ex-validrefs-fits-stronger (previous step)

validrefs(str, r ' + refs0, ty, st), is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, ∀ st, ty, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, ty, st) → (∃ sks. fits(r, sks, st) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs)[n]))) ⊦ r = jvmref, ∃ sks. fits(r, sks, st) ∧ # sks = # refs0 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 58:
validrefs(str, r ' + refs0, ty, st), is_obj(str, r, st) ∨ is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ st, ty, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, ty, st) → (∃ sks. fits(r, sks, st) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs)[n]))) ⊦ r = jvmref, ∃ sks. fits(r, sks, st) ∧ # sks = # refs0 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n])

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [st, r, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]