Commit d890fc82 by Samuel Ben Hamou

### Ajout de tactiques utiles pour raccourcir les preuves.

parent 5135e686
 ... ... @@ -182,6 +182,16 @@ Qed. Ltac axiom := apply R_Ax; compute; intuition. Ltac app_R_All_i t := apply R_All_i with (x := t); [ rewrite<- Names.mem_spec; now compute | ]. Ltac sym := apply Symmetry; [ auto | auto | compute; intuition | ]. Ltac hered := apply Hereditarity; [ auto | auto | compute; intuition | ]. Ltac ahered := apply AntiHereditarity; [ auto | auto | compute; intuition | ]. Ltac trans b := apply Transitivity with (B := b); [ auto | auto | auto | compute; intuition | assumption | assumption ]. (** Some basic proofs in Peano arithmetics. *) Lemma ZeroRight : IsTheorem Intuiti PeanoTheory (∀ (#0 = #0 + Zero)). ... ... @@ -246,7 +256,7 @@ Proof. apply R_All_e with (t := FVar "y") in AX9; [ | auto ]. compute in AX9. assumption. } assert (Pr Intuiti (AxRec :: axioms_list ⊢ Succ (Zero + FVar "y") = Succ (FVar "y"))). { apply Hereditarity; [ auto | auto | compute; intuition | assumption ]. } { hered. assumption. } assert (Pr Intuiti (AxRec :: axioms_list ⊢ ax9)). { apply R_Ax. compute; intuition. } unfold ax9 in H1. ... ... @@ -281,7 +291,7 @@ Proof. apply R_All_e with (t := FVar "y") in H1; [ | auto ]. cbn in H1. apply Hereditarity in H1; [ | auto | auto | compute; intuition ]. apply Transitivity with (B := Succ (Succ ( FVar "x" + FVar "y"))); [ auto | auto | auto | compute; intuition | assumption | assumption ]. trans (Succ (Succ ( FVar "x" + FVar "y" ))). Qed. Lemma Comm : IsTheorem Intuiti PeanoTheory (∀∀ (#0 + #1 = #1 + #0)). ... ...
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