Suppose you are given the following axioms: (a) 0 ≤ 3. (b) 7 ≤ 9. (c) ∀x: x ≤ x. (d) ∀x: x ≤ x + 0. (e) ∀x: x + 0 ≤ x. (f) ∀x, y : x + y ≤ y + x. (g) ∀w, x, y, z : w ≤ y ∧ x ≤ z → w + x ≤ y + z. (h) ∀x, y, z : x ≤ y ∧ y ≤ z → x ≤ z. Give a forward-chaining proof of the sentence 7 ≤ 3 + 9. Show only the steps that lead to success

时间: 2024-04-03 20:35:39 浏览: 95
PPTX

大学六级英语写作实用词汇汇总.pptx

1. By (a), we have 0 ≤ 3. 2. By (e), we have 3 + 0 ≤ 3. 3. By (d), we have 3 ≤ 3 + 0. 4. By (b), we have 7 ≤ 9. 5. By (g) with w=7, x=0, y=9, and z=3, we have 7 + 0 ≤ 9 + 3. 6. By (f), we have 0 + 7 ≤ 3 + 9. 7. Therefore, 7 ≤ 3 + 9.
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资源摘要信息:"易语言是一种基于中文的编程语言，主要面向中文用户，其特点是使用中文关键词和语法结构，使得中文使用者更容易理解和编写程序。易语言画板图像缩放源码是易语言编写的程序代码，用于实现图形用户界面中的画板组件上图像的缩放功能。通过这个源码，用户可以调整画板上图像的大小，从而满足不同的显示需求。它可能涉及到的图形处理技术包括图像的获取、缩放算法的实现以及图像的重新绘制等。缩放算法通常可以分为两大类：高质量算法和快速算法。高质量算法如双线性插值和双三次插值，这些算法在图像缩放时能够保持图像的清晰度和细节。快速算法如最近邻插值和快速放大技术，这些方法在处理速度上更快，但可能会牺牲一些图像质量。根据描述和标签，可以推测该源码主要面向图形图像处理爱好者或专业人员，目的是提供一种方便易用的方法来实现图像缩放功能。由于源码文件名称为'画板图像缩放.e'，可以推断该文件是一个易语言项目文件，其中包含画板组件和图像处理的相关编程代码。" 易语言作为一种编程语言，其核心特点包括： 1. 中文编程：使用中文作为编程关键字，降低了学习编程的门槛，使得不熟悉英文的用户也能够编写程序。 2. 面向对象：易语言支持面向对象编程（OOP），这是一种编程范式，它使用对象及其接口来设计程序，以提高软件的重用性和模块化。 3. 组件丰富：易语言提供了丰富的组件库，用户可以通过拖放的方式快速搭建图形用户界面。 4. 简单易学：由于语法简单直观，易语言非常适合初学者学习，同时也能够满足专业人士对快速开发的需求。 5. 开发环境：易语言提供了集成开发环境（IDE），其中包含了代码编辑器、调试器以及一系列辅助开发工具。 6. 跨平台：易语言支持在多个操作系统平台编译和运行程序，如Windows、Linux等。 7. 社区支持：易语言有着庞大的用户和开发社区，社区中有很多共享的资源和代码库，便于用户学习和解决编程中遇到的问题。 在处理图形图像方面，易语言能够： 1. 图像文件读写：支持常见的图像文件格式如JPEG、PNG、BMP等的读取和保存。 2. 图像处理功能：包括图像缩放、旋转、裁剪、颜色调整、滤镜效果等基本图像处理操作。 3. 图形绘制：易语言提供了丰富的绘图功能，包括直线、矩形、圆形、多边形等基本图形的绘制，以及文字的输出。 4. 图像缩放算法：易语言实现的画板图像缩放功能中可能使用了特定的缩放算法来优化图像的显示效果和性能。 易语言画板图像缩放源码的实现可能涉及到以下几个方面： 1. 获取画板上的图像：首先需要从画板组件中获取到用户当前绘制或已经存在的图像数据。 2. 图像缩放算法的应用：根据用户的需求，应用适当的图像缩放算法对获取的图像数据进行处理。 3. 图像重新绘制：处理后的图像数据需要重新绘制到画板上，以实现缩放后的效果。 4. 用户交互：提供用户界面，让用户能够通过按钮、滑块等控件选择缩放比例和模式，以及触发缩放操作。 5. 性能优化：为了确保图像缩放操作流畅，需要考虑代码的执行效率和资源的合理利用。 在易语言社区中，用户可以根据自己的需求修改和扩展画板图像缩放源码，或者根据提供的API进一步开发更多高级图像处理功能，从而丰富软件的功能和用户体验。