// This prints the left floatting menu
Dedukti    Load Matita      Load Coq         Load Lean        Load PVS         Load OpenTheory Load
Dedukti-jumb

Theorem

cong.congruent_n_mod_n

Statement

∀ n p, O < p ⇒ n ≡ (mod n p) [p]

Main Dependencies
definition
Theory

Coq-Jumb
Statement

Theorem congruent_n_mod_n : forall (n:nat.nat), forall (p:nat.nat), (nat.lt nat.O p) -> congruent n (div_mod.mod n p) p.



Matita-Jumb
Statement

theorem congruent_n_mod_n : \forall (n:nat). \forall (p:nat). ((lt) (O) p) -> (congruent) n ((mod) n p) p.



Lean-jumb
Statement

theorem congruent_n_mod_n : forall (n:nat.nat) , forall (p:nat.nat) , ((((nat.lt_) ) ((nat.O) )) (p)) -> ((((cong.congruent) ) (n)) ((((div_mod.mod) ) (n)) (p))) (p).



PVS-jumb

Statement

congruent_n_mod_n : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):(FORALL(p:nat_sttfa_th.sttfa_nat):(nat_sttfa_th.lt(nat_sttfa_th.sttfa_O)(p) => cong_sttfa.congruent(n)(div_mod_sttfa_th.mod(n)(p))(p))))



OpenTheory

Printing for OpenTheory is not working at the moment.