Environment Insertion Guide

This guide will walk you through creating Theorems, Lemmas, Propositions, and Proofs using Enunciations.

Instructions

To insert the theorem environment:

Click sequentially in the toolbar: Insert -> Enunciation -> Theorem

Tips for using theorems:

• Place the cursor on the Enunciation you added
• Type theorem content
• To exit the theorem environment, use Ctrl+Shift+Backspace

Available Enunciation Types

In Liii STEM, you can directly insert the following Enunciation types:

• Axiom - Basic principles or assumptions
• Definition - Clear explanations of concepts
• Theorem - Fundamental mathematical statements
• Proposition - General mathematical assertions
• Lemma - Supporting results for main theorems
• Corollary - Direct consequences of theorems
• Conjecture - Unproven mathematical statements
• Example - Illustrative instances
• Problem - Mathematical questions or exercises
• Proof - Logical demonstrations of statements
• Solution - Answers to problems
• Remark - Additional observations or comments

Feature Introduction

This feature provides standardized writing environments for Theorems, Lemmas, Corollaries, Propositions, and Proofs using Enunciations.

Detailed Instructions

Click sequentially in the toolbar: Insert -> Enunciation -> Theorem
(You can choose lemma, corollary, proposition, proof, and other environments as needed) (as shown in the image below)

Note: If you need more diverse numbering or environment format requirements, please follow these steps for further operations:

• Place the cursor on the Enunciation you added
• Click sequentially in the toolbar: Focus -> Preferences (as shown in the image below)
• Select the numbering or environment format you need. The specific format explanations are shown in the table below:
  

Format Name	Description
European numbering style	Set European style
Prefix by section number	Add section hierarchy
Framed theorems	Add frame
Hanging theorems	Add floating frame

Examples

1. Theorem: Core conclusion that requires rigorous proof, representing the main contribution of the article.
   
2. Lemma: Auxiliary conclusion that provides intermediate steps for proving theorems or propositions.
   
3. Corollary: Direct extension result of theorems or propositions, often requiring brief supplementary proof.
4. Proposition: Independent conclusion of less importance than theorems, can be viewed as small theorems or unnamed theorems.
   
5. Proof: Logical reasoning process that verifies the correctness of theorems, lemmas, propositions, or corollaries.
   

Important Notes

1. The presentation effect of the same Enunciation differs in different language modes. For example, the content in "Theorem" appears in normal style in Chinese mode, while it appears in italics in English mode.
2. Please try to use Enunciations independently and avoid nesting one Enunciation within another Enunciation.