[isabelle] mod_add1_eq - Theory Divides


Just wondering if there is a problem with the lemma "mod_add1_eq"(see below) in the theory Divides.

(* Snippet from the divides theory which I am not able to verify*)

lemma mod_add1_eq: "(a+b) mod (c::nat) = (a mod c + b mod c) mod c"
apply (case_tac "c = 0", simp)
apply (blast intro: quorem_div_mod quorem_div_mod
                   quorem_add1_eq [THEN quorem_mod])

(* end of snippet *)

Iam finding it a bit difficult to get this verified. Iam a new-comer both to Isabelle and to theorem verification, so if I have missed out on something really primitive, apologies for taking your time.

Is there an easier way to verify "(a+b) mod (c::nat) = (a mod c + b mod c) mod c", though?


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