Difference between revisions of "Rodin Proof Tactics"

From Event-B
Jump to navigationJump to search
imported>Son
imported>Son
Line 422: Line 422:
  
 
== disjE ==
 
== disjE ==
−
 
−
== Remove Negation in Goal ==
 
  
 
== allE ==
 
== allE ==
Line 435: Line 433:
 
== cont Implication Hypothesis ==
 
== cont Implication Hypothesis ==
  
−
== Functional Overriding in Goal ==
+
== Functional Overriding ==
−
 
 
−
== Functional Overriding in Hypothesis ==
 
  
 
== Equality ==
 
== Equality ==
Line 443: Line 439:
 
== Modus Tollens ==
 
== Modus Tollens ==
  
−
== Remove Membership in Hypothesis ==
+
== Remove Membership ==
−
 
 
−
== Remove Membership in Goal ==
 
−
 
 
−
== Remove Inclusion in Hypothesis ==
 
−
 
 
−
== Remove Inclusion in Goal ==
 
−
 
 
−
== Remove Strict-Inclusion in Hypothesis ==
 
−
 
 
−
== Remove Strict-Inclusion in Goal ==
 
  
−
== Inclusion Set Minus Right in Hypothesis ==
+
== Remove Inclusion ==
  
−
== Inclusion Set Minus Right in Goal ==
+
== Remove Strict-Inclusion ==
  
−
== Remove Inclusion Universal in Hypothesis ==
+
== Inclusion Set Minus Right ==
  
−
== Remove Inclusion Universal in Goal ==
+
== Remove Inclusion Universal ==
  
 
== Implication Introduction ==
 
== Implication Introduction ==
  
−
== Disjunction to Implication in Hypothesis ==
+
== Disjunction to Implication ==
−
 
 
−
== Disjunction to Implication in Goal ==
 
  
 
== Forall Modus Ponens ==
 
== Forall Modus Ponens ==
Line 483: Line 467:
 
== impOrGoal ==
 
== impOrGoal ==
  
−
== relImgUnionRight Hypothesis ==
+
== relImgUnionRight ==
−
 
 
−
== relImgUnionRight Goal ==
 
−
 
 
−
== relImgUnionLeft Hypothesis ==
 
−
 
 
−
== relImgUnionLeft Goal ==
 
−
 
 
−
== Set Equality in Hypothesis ==
 
−
 
 
−
== Set Equality in Goal ==
 
−
 
 
−
== Equivalent in Hypothesis ==
 
−
 
 
−
== Equivalent in Goal ==
 
  
−
== Functional Intersection Image in Hypothesis ==
+
== relImgUnionLeft ==
  
−
== Functional Intersection Image in Goal ==
+
== Set Equality ==
  
−
== Functional Set Minus Image in Hypothesis ==
+
== Equivalent ==
  
−
== Functional Set Minus Image in Goal ==
+
== Functional Intersection Image ==
  
−
== Functional Singleton Image in Hypothesis ==
+
== Functional Set Minus Image ==
  
−
== Functional Singleton Image in Goal ==
+
== Functional Singleton Image ==

Revision as of 08:10, 7 March 2010

This page contains descriptions of the available proof tactics within the RODIN Platform.

For each tactic, the descriptions is as follows:

  • Description: A high-level description of the tactic
  • ID: An unique ID associated with the tactic.
  • Display: How an application of the tactic is displayed in the proof tree, the auto-tactic preference or the post-tactic preference.
  • Auto-tactic: No: the tactic cannot be added as an auto-tactic. Yes: the tactic can be added as an auto-tactic. Default: the tactic is a default auto-tactic.
  • Post-tactic: No: the tactic cannot be added as a post-tactic. Yes: the tactic can be added as a post-tactic. Default: the tactic is a default post-tactic.
  • Interactive: No: the tactic cannot be invoked interactively. Global: The tactic can be invoked from the Proof Control. Goal: The tactic can be invoked from the goal view. Hypothesis: The tactic can be invoked from the hypothesis view. If the tactic can be invoked interactively (i.e. either Global, Goal or Hypothesis), more information about how this could be done will be given. Note that since the Post-tactics can be launched manually, any tactics that can be included in the post-tactic in principle can be invoked interactively via the post-tactic. No here mean that there is no separate invocation for this specific tactic.
  • Example: Example(s) on how the tactic can be seen from the RODIN Platform.

Contents

True Goal

  • Description: Discharges any sequent whose goal is '⊤' (logical true).
  • ID: org.eventb.core.seqprover.trueGoalTac
  • Display: ⊤ Goal
  • Auto-tactic: Default
  • Post-tactic: Default
  • Interactive: No
  • Example: TODO

False Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Goal in Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Goal Disjunct in Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Functional Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Simplification Rewriter

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Type Rewriter

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Implication Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

For-all Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Exists Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Find Contradictory Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Use Equality Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Shrink Implicative Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Shrink Enumerated Set

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Implicative Hypothesis with Conjunctive RHS

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Implicative Hypothesis with Disjunctive LHS

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Conjunctive Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Clarify Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Functional Overriding in Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Functional Overriding in Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Partition Rewriter

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

One-Point Rule in Goal

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

One-Point Rule in Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Bounded Goal with Finite Hypothesis

  • Description: TODO
  • ID: TODO
  • Display: TODO
  • Auto-tactic: TODO
  • Post-tactic: TODO
  • Interactive: TODO
  • Example: TODO

Falsify Goal

conjI

allI

exI

Remove Negation

Review

Proof by cases

Add Hypothesis

Abstract Expression

Automatic Prover

Post tactic

Lasoo

Back Tracking

Prune

Search Hypothesis

Cache Hypothesis

Previous

Next

Information

Falsify Hypothesis

Modus Ponens

conjE

disjE

allE

exE

eq1

Double Implication Hypothesis

cont Implication Hypothesis

Functional Overriding

Equality

Modus Tollens

Remove Membership

Remove Inclusion

Remove Strict-Inclusion

Inclusion Set Minus Right

Remove Inclusion Universal

Implication Introduction

Disjunction to Implication

Forall Modus Ponens

Next Pending Sub-goal

Next Reviewed Sub-goal

impAndHyp

impAndGoal

impOrHyp

impOrGoal

relImgUnionRight

relImgUnionLeft

Set Equality

Equivalent

Functional Intersection Image

Functional Set Minus Image

Functional Singleton Image

Retrieved from ‘https://wiki.event-b.org/index.php?title=Rodin_Proof_Tactics&oldid=8435’