Formalize a set theory argumentation from a short story fiction This problem may be interesting. A writer Raymond Queneau wrote in his "Exercises in Style" a series of stories depicting the same event. One of them was in set theory. I'm wondering if anyone might be able and interested to formulate these events in standard set theory notation? This may be used as part of illustrative materials for a theatre project. Thanks a lot!

Set Theory
On the S bus, let us consider the set Ƨ of seated passengers and the
  set U of upright passengers.  At a particular stop is located the set
  P of people that are waiting.  Let C be the set of passengers that get
  on; this is a subset of P and is itself the union of the set Cʹ of
  passengers that remain on the platform and of the set C ̋ of those who
  go and sit down.  Demonstrate that the set C ̋ is empty. H being the
  set of cool cats and {ɦ} the intersection of H and of Cʹ, reduced to a
  single element.  Following the surjection of the feet of ɦonto those
  of y (any element of Cʹ that differs from ɦ), the yield is the set W
  of words pronounced by the element ɦ.  Set C ̋  having become
  non-empty, demonstrate that it is composed of the single element ɦ.
Now let Pʹ equal the set of pedestrians to be found in front of the
  Gare Saint-Lazare, {ɦ, ɦʹ} the intersection of H and of Pʹ, B being
  the set of buttons on the overcoat belonging to ɦ, Bʹ the set of
  possible locations of said buttons according to ɦʹ, demonstrate that
  the injection of B into Bʹ is not a bijection.
—Raymond Queneau Translated by Chris Clarke (source)

 A: Let A be the set of seated passengers (voyageurs assis) and D those that are
standing.
Lemma.
 $A \not = \emptyset$.
Proof. That some passengers on the bus are standing is a consequence of the
fact that this is the rush-hour  (une heure d'affluence), and surely a result
of the poor transportation service at that time. QED
Now if C is the set of people waiting in the bus-stop that were able to get on the bus, define $C' = C\cap D$ (namely those forced to stay standing on the platform) and $C^{''} = C \cap A$ (those who found a sitting place). We have to show that $C''=\emptyset$. Well, it follows from the axiom of selfishness that the platform passengers will not let those of C (the ``newcomers'') to sit unless they find a place for themselves. Hence trivially $C^{''} = \emptyset$.
Let $z$ be the unique cool-cat on the platform (zazou) and $y\in C'$ another
passenger on the platform. Let $feet(p)$ denote the feet of $p$, and S the stepping relation. We have that $\langle feet(y), feet(z)\rangle\in S$, or in a more direct expression ''y steps on z''.
This implies immediately a two-phase reaction by z. A set of words W followed
by establishing $z\in C^{''}$ (namely z rushes to find a sitting place).  Queneau concludes that $C^{''} = \{ z \}$ and asks for a proof of this statement. It is I believe an erroneous conclusion hastily made. The evidence that ''z abandonna rapidement la discussion pour se jeter sur une place devenue libre'' does not imply that other passengers were unable to find a place. (A counterexample is easy to build.) 
Finally, the statement about the buttons is a direct consequence of the button hole principle. 
