R – How to write ∀x ( P(x) and Q(x) ) in Coq


I'm trying out Coq, but I'm not completely sure what I'm doing. Is:

Theorem new_theorem : forall x, P:Prop /\ Q:Prop

Equivalent to:

∀x ( P(x) and Q(x) )

Edit: I think they are.

Best Solution

Are you having problems with the syntax?

$ coqtop
Welcome to Coq 8.1pl3 (Dec. 2007)

Coq < Section Test.

Coq < Variable X:Set.
X is assumed

Coq < Variables P Q:X -> Prop.
P is assumed
Q is assumed

Coq < Theorem forall_test: forall x:X, P(x) /\ Q(x).
1 subgoal

  X : Set
  P : X -> Prop
  Q : X -> Prop
   forall x : X, P x /\ Q x

forall_test < 
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