4.11 Special Contradiction

Attempt to prove by contradiction without automatic raising of hypotheses

Syntax

  cts

Use

This command enables to attempt a proof by contradiction, without automatic raising of hypotheses.
If the current goal is G, it is then transformed into:
  ¬G bfalse
The hypotheses, completed by ¬G, must be able to generate bfalse.
This command is identical to ct, except that the generated hypotheses are not automatically raised.

Example

Let us consider the following proof obligation:


 
    Hypothesis  
        ENS = {e1,e2,e3,e4,e5} &  
        tt: ENS &  
        uu: ENS &  
        not(uu = tt) &  
        uu: {e1,e2,e3,e4} => tt = e5 &  
        uu = e5 => tt = e1  
    Goal  
        not(e2 = e5)  
 


We attempt a proof by contradiction, given the form of the goal.


 
PRI> cts  
Starting Contradiction  
 


¬¬e2 = e5 is simplified in e2 = e5. The goal becomes:


 
    Goal  
        e2=e5 => bfalse