4.18 False hypothesis

Attempt to prove using contradictory hypotheses

Syntax

  fh(h)

with:

Use

this command enables to perform a demonstration, by proving that a hypothesis is contradictory to the others.

If the lemma to be demonstrated is
  G under the hypotheses h1 , , hn
and the user suspects that one of the hypotheses hi is contradictory to the others, we can demonstrate the lemma by demonstrating:
  ¬hi under the hypotheses h1, ,hn

Example

Given the following situation:


 
    Hypothesis  
        ENS = {e1,e2,e3,e4,e5} &  
        e2 = e5  
    Goal  
        e5 = e1  
 


It is clear that the hypothesis e2 = e5 is contradictory. By applying the command:


 
PRI> fh(e2=e5)  
Starting False Hypothesis  
 


the current goal becomes:


 
    Goal  
        not(e2 = e5)  
 


by calling the automatic prover the goal can then be discharged.


 
PRI> pr  
Starting Prover Call