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Proof step 20 from proof pathex-array (previous step)

validrefs(str, refs, st[refs .first -- _type] .type, st), is_array(str, refs .first, st) ⊦ refs .first = refs .last, refs = [], ∃ i. ¬ i < 0 ∧ ¬ st[refs .first -- _length] .intval ≤ i ∧ is_referencevalue(st[refs .first -- i ']) ∧ ( st[refs .first -- i '] .refval ≠ jvmref ∧ st[st[refs .first -- i '] .refval -- _type] .type ≤ st[refs .first -- _type] .type .type ∧ path∃(str, st[refs .first -- i '] .refval, refs .last, st) ∨ st[refs .first -- i '] .refval = jvmref ∧ refs .last = jvmref)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
refs = r + refs0, validrefs(str, refs, st[r -- _type] .type, st), is_array(str, r, st) ⊦ r = refs .last, refs = [], ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, refs .last, st) ∨ st[r -- i '] .refval = jvmref ∧ refs .last = jvmref)

Rule argument

[speclemmaarg: ,refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) ,[refs, r, refs0] → [refs, r, refs0] ,T ,list-data ,references-olista ,elim-1 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs, r, refs0)]]