alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
alias id "not" = "cic:/Coq/Init/Logic/not.con".
-
+alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
+alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con".
theorem a :
\forall A:Set.
intros. simplify. change in \vdash (? ? (? %) ?) with O.
reflexivity. qed.
+
theorem X: \forall x:nat. let myplus \def plus x in myplus (S O) = S x.
- intros. simplify. change in \vdash (? ? (% ?) ?) with plus x.
- rewrite > plus_comm. reflexivity. qed.
+ intros. simplify. change in \vdash (? ? (% ?) ?) with (plus x).
+
+rewrite > plus_comm. reflexivity. qed.
theorem R: \forall x:nat. let uno \def x + O in S O + uno = 1 + x.
intros. simplify.
- change in \vdash (? ? (? %) ?) with x + O.
+ change in \vdash (? ? (? %) ?) with (x + O).
rewrite > plus_comm. reflexivity. qed.