Difference between revisions of "Maplet Overriding in Goal"

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imported>Billaude
(New page: This page describes the design of a tactic requested here : [https://sourceforge.net/tracker/index.php?func=detail&aid=3306228&group_id=108850&atid=651672 Feature Request #3306228] = Obje...)
 
imported>Billaude
Line 3: Line 3:
 
= Objective =
 
= Objective =
  
Split every goal in the form : <math> f \ovl{\left\{x \mapsto y\right\}} \in A \to B </math> into three sub-goals :
+
Split every goal in the form : <math> f \ovl{\{x \mapsto y\}} \in A \to B </math> into three sub-goals :
:*<math>{x} \domsub f \in A \smallsetminus \left\{x\right\} \to B</math>
+
:*<math>\{x\} \domsub f \in A \smallsetminus \{x\} \to B</math>
 
:*<math>x \in A</math>
 
:*<math>x \in A</math>
 
:*<math>y \in B</math>
 
:*<math>y \in B</math>

Revision as of 13:08, 30 May 2011

This page describes the design of a tactic requested here : Feature Request #3306228

Objective

Split every goal in the form :  f \ovl{\{x \mapsto y\}} \in A \to B into three sub-goals :

  • \{x\} \domsub f \in A \smallsetminus \{x\} \to B
  • x \in A
  • y \in B

Design Decision

Instead of proofing the first sub-goal, it may be more easy to proof f\in A\to B which is a sufficient condition : (f\in A\to B)\limp ({x} \domsub f \in A \smallsetminus \left\{x\right\} \to B).

Implementation

First, the goal is checked. Its tree structure must match the following one :

\in
├── \ovl
│   ├── f
│   └── {}
│       └──  \mapsto
│            ├── x
│            └── y
└── \to
    ├── A
    └── B

Then, if the hypothesis f\in A\to B is contained in the hypothesis the goal is splitted as follows :

  • f\in A\to B
  • x \in A
  • y \in B

Else, it is splitted as follows :

  • {x} \domsub f \in A \smallsetminus \left\{x\right\} \to B
  • x \in A
  • y \in B