[>bigop_Strue // >Hind >bigop_sum @same_bigop
#i #lti @leb_elim // #lei cut (i = n*k2+(i-n*k2)) /2/
#eqi [|#H] (>eqi in ⊢ (???%))
- >div_plus_times /2/ >Hp1 >(mod_plus_times …) /2/
+ >div_plus_times /2/ >Hp1 >(mod_plus_times …) /2/ normalize //
|>bigop_Sfalse // >Hind >(pad_bigop (S n*k2)) // @same_bigop
#i #lti @leb_elim // #lei cut (i = n*k2+(i-n*k2)) /2/
#eqi >eqi in ⊢ (???%) >div_plus_times /2/
]
qed.
+(*
theorem binomial_law:∀a,b,n.
(a+b)^n = Σ_{k < S n}((bc n k)*(a^(n-k))*(b^k)).
#a #b #n (elim n) //
rewrite < sym_plus.
reflexivity.
qed. *)
-
+*)
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(* *)
(**************************************************************************)
+(* To be ported
include "nat/primes.ma".
include "nat/lt_arith.ma".
apply ex_m_le_n_nth_prime_m.
simplify.unfold prime in H.elim H.assumption.
qed.
-
+*)
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\ /
V_______________________________________________________________ *)
+(* To be ported
include "arithmetics/bigops.ma".
definition natAop ≝ mk_Aop nat 0 plus (λa.refl ? a) (λn.sym_eq ??? (plus_n_O n))
|assumption
]
]
-qed. *)
\ No newline at end of file
+qed. *)*)
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