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[mukesh tiwari <mukeshtiwari.iiitm AT gmail.com>]

Hi Everyone,

Pardon me if this is stupid question, but I am trying to understand the difference between dot (.) and semicolon (;) in Coq. My understanding is that we can interchange the dot and semicolon in Coq file. If you add dot after each tactic then you see the intermediate steps/calculation after applying the tactic to goal, and if you don't want to see the intermediate steps then use semicolon to combine multiple tactics.

Currently I am trying to go though the coq-graph [1] code.

 
   Lemma Union_dec :
     forall (e1 e2 : U_set) (x : U),
       {e1 x} + {~ e1 x} -> {e2 x} + {~ e2 x} -> Union e1 e2 x -> {e1 x} + {e2 x}.
   Proof.
     intros; case H.
     left; trivial.

     intros; case H0; intros.
     right; trivial.

     absurd (Union e1 e2 x). apply Not_union; trivial.
     trivial.

   Qed.

If I replace all the semicolons by dots then It is not provable by following the same tactics.

Lemma Union_dec :
     forall (e1 e2 : U_set) (x : U),
       {e1 x} + {~ e1 x} -> {e2 x} + {~ e2 x} -> Union e1 e2 x -> {e1 x} + {e2 x}.
   Proof.
     intros. case H.
     left. trivial.

     intros. case H0. intros.
     right. trivial.

     absurd (Union e1 e2 x). apply Not_union. trivial.
     trivial.

and goal is

  
  U : Set
  e1, e2 : U_set
  x : U
  H : {e1 x} + {~ e1 x}
  H0 : {e2 x} + {~ e2 x}
  H1 : Union e1 e2 x
  n : ~ e1 x
  ============================
   ~ e2 x

subgoal 2 (ID 51) is:
 Union e1 e2 x


Regards,
Mukesh Tiwari

[1] https://github.com/coq-contribs/graph-basics/blob/master/Sets.v