Commit 05819e8d authored by Samuel Ben Hamou's avatar Samuel Ben Hamou
Browse files

ZeroRight, la suite (et bientôt la fin j'espère).

parent fa3e1a03
......@@ -130,13 +130,14 @@ Proof.
-- reflexivity.
-- reflexivity.
-- set (hyp := (_ -> _)%form). change (Fun "O" []) with Zero. change (Zero + Zero = Zero) with (bsubst 0 Zero (Zero + #0 = #0)). apply R_All_e. reflexivity. apply R_Ax. compute; intuition.
++ cbn. change (Fun "O" []) with Zero. apply R_All_i with (x := "x"). (* ax4 et ax10 +- sym *)
++ cbn. change (Fun "O" []) with Zero. apply R_All_i with (x := "y"). (* ax4 et ax10 +- sym *)
-- compute. inversion 1.
-- cbn. change (Fun "O" []) with Zero. apply R_Imp_i. set (H1 := FVar _ = _). set (H2 := _ -> _).
assert (hyp : Pr Intuiti (H1 :: H2 :: axioms_list Fun "S" [FVar "x"] = Fun "S" [FVar "x" + Zero] /\ Fun "S" [FVar "x" + Zero] = Fun "S" [FVar "x" + Zero])).
{ admit. }
apply R_Imp_e with (A := Fun "S" [FVar "x"] = Fun "S" [FVar "x" + Zero] /\ Fun "S" [FVar "x" + Zero] = Fun "S" [FVar "x" + Zero]).
** apply R_All_i with (x := Fun "S" [FVar "x"]).
assert (hyp : Pr Intuiti (H1 :: H2 :: axioms_list Fun "S" [FVar "y"] = Fun "S" [FVar "y" + Zero] /\ Fun "S" [FVar "y" + Zero] = Fun "S" [FVar "y"] + Zero)).
{ apply R_And_i.
+ apply R_Imp_e with (A := (FVar "y" = FVar "y" + Zero)%form); [ | apply R_Ax; compute; intuition ]. apply R_All_e with (t := FVar "y"). }
apply R_Imp_e with (A := Fun "S" [FVar "y"] = Fun "S" [FVar "y" + Zero] /\ Fun "S" [FVar "y" + Zero] = Fun "S" [FVar "y"] + Zero).
** apply R_All_i with (x := "Fun "" ++ "S" ++ ""[FVar"" ++ "y" ++ ""]").
Lemma Comm : IsTheorem Intuiti PeanoTheory (∀∀ (#0 + #1 = #1 + #0)).
Proof.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment