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Proof step 62 from proof ex-validrefs-fits-stronger (previous step)

validrefs(str, r ' + refs0, ty, st), ∀ 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 ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty), ∃ 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 2:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 60:
r ≠ jvmref, validrefs(str, r ' + refs0, ty, st), ∀ 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 ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty), ∃ sks. fits(r, sks, st) ∧ # sks = # refs0 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n])
Proof step 61:
⊦ fits(jvmref, sks, st) ↔ sks = []

Rule argument

[speclemmaarg: ,r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = []) ,[st, ty, refs, r, str] → [st, ty, refs0, r, str] ,F ,cyclic , ,validrefs-null ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ m ≤ 0 ↔ m = 0])], [EXTRATERMS : (st, ty, refs0, r, str)]]