Johannes Hölzl Jannis Limperg The Hitchhiker’s Guide to Logical Verification 2021 Standard Edition (October 13, 2021) lean-forward.github.io/ logical-verification/2021 ii Contents Contents iii Preface Predicates 75 5.1 Introductory Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Logical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Rule Induction . A Simpler Approach Based on an Inductive Predicate . . . . . . . . . 164 IV Mathematics 165 11 Logical Foundations of Mathematics 167 11.1 Universes . . . . . . . . . . . . . . . . . . . . . . . . .

scenarios by providing diverse table types. Logic Table The logical name of the horizontally sharded database (table) of the same structure is the logical identi‐ fier of the table in SQL. Example: Order data split into 10 tables according to the primary key endings, are t_order_0 to t_order_9, and their logical table names are t_order. Actual Table Physical tables that exist in the horizontally sharded databases multiple sharding rules in the binding table need to be configured according to the combination of logical table prefix and sharding suffix, for example: rules: - !SHARDING tables: t_order: actualDataNodes:

scenarios by providing diverse table types. Logic Table The logical name of the horizontally sharded database (table) of the same structure is the logical identi‐ fier of the table in SQL. Example: Order data split into 10 tables according to the primary key endings, are t_order_0 to t_order_9, and their logical table names are t_order. Actual Table Physical tables that exist in the horizontally sharded databases multiple sharding rules in the binding table need to be configured according to the combination of logical table prefix and sharding suffix, for example: rules: - !SHARDING tables: t_order: actualDataNodes:

scenarios by providing diverse table types. Logic Table The logical name of the horizontally sharded database (table) of the same structure is the logical identi‐ fier of the table in SQL. Example: Order data split into 10 tables according to the primary key endings, are t_order_0 to t_order_9, and their logical table names are t_order. Actual Table Physical tables that exist in the horizontally sharded databases source name and the real table. Example: ds_0.t_order_0. The mapping relationship between the logical table and the real table can be classified into two forms: uniform distribution and custom distribution

scenarios by providing diverse table types. Logic Table The logical name of the horizontally sharded database (table) of the same structure is the logical identi‐ fier of the table in SQL. Example: Order data split into 10 tables according to the primary key endings, are t_order_0 to t_order_9, and their logical table names are t_order. Actual Table Physical tables that exist in the horizontally sharded databases source name and the real table. Example: ds_0.t_order_0. The mapping relationship between the logical table and the real table can be classified into two forms: uniform distribution and custom distribution

Operators .................................................................................. 221 9.1. Logical Operators ................................................................................ 221 9 Internals ................................................................................... 885 29. Logical Replication .................................................................................... ............................ 1522 47. Logical Decoding ........................................................................................ 1525 47.1. Logical Decoding Examples ...................

...................................................................................... 234 9.1. Logical Operators ...................................................................................... ....................................................................................... 933 29. Logical Replication .................................................................................... ......................... 1602 47. Logical Decoding ............................................................................................. 1606 47.1. Logical Decoding Examples .................

Foreign Keys to Physical Model 40 Chapter 6 - Logical Model 41 About Logical Models 41 Add Entities to Logical Model 41 Add a Relation to a Logical Model 43 Chapter 7 - Conceptual Model 45 Linux. Here are some highlights of Navicat Data Modeler: • Create and manipulate conceptual/logical/physical models. • Support various database systems: MySQL, MariaDB, Oracle, PostgreSQL, SQLite top of the Main Window. The buttons display in the toolbar depend on the model type (physical, logical and conceptual). You can use the toolbar to perform some basic tasks, such as adding tables, entities

Operators .................................................................................. 219 9.1. Logical Operators ................................................................................ 219 9 Internals ................................................................................... 861 31. Logical Replication .................................................................................... ............................ 1485 49. Logical Decoding ........................................................................................ 1488 49.1. Logical Decoding Examples ...................

...................................................................................... 231 9.1. Logical Operators ...................................................................................... ....................................................................................... 905 31. Logical Replication .................................................................................... ......................... 1565 49. Logical Decoding ............................................................................................. 1569 49.1. Logical Decoding Examples .................