metamath1

Usage

Overview

metamath is a formal proof verifier and proof assistant for the Metamath language. It can be initialized via a series of commands or with a data base file, which can then be explored interactively.

For details about the Metamath language and the command-line interface, type help into the command prompt, or read the Metamath book [1], which should have been installed along with the package.

Language

A Metamath database consists of a sequence of three kinds of tokens separated by white space (which is any sequence of one or more white space characters). The set of keyword tokens is ${, $}, $c, $v, $f, $e, $d, $a, $p, $., $=, $(, $), $[, and $]. The latter four are called auxiliary or preprocessing keywords. A label token consists of any combination of letters, digits, and the characters hyphen, underscore, and period. The label of an assertion is used to refer to it in a proof. A math symbol token may consist of any combination of the 93 printable ascii(7) characters other than $. All tokens are case-sensitive.

$( comment $)

Comments are ignored.

$[ file $]

Include the contents of a file.

${ statements $}

Scoped block of statements. A math symbol becomes active when declared and stays active until the end of the block in which it is declared.

$v symbols $.

Declare symbols as variables. A variable may not be declared a second time while it is active, but it may be declared again (as a variable, but not as a constant) after it becomes inactive.

$c symbols $.

Declare symbols as constants. A constant must be declared in the outermost block and may not be declared a second time.

label $f constant variable $.

Variable-type hypothesis to specify the nature or type of a variable (such as `let x be an integer.'). A variable must have its type specified in a $f statement before it may be used in a $e, $a, or $p statement. There may not be two active $f statements containing the same variable.

label $e constant symbols $.

Logical hypothesis, expressing a logical truth (such as `assume x is prime') that must be established in order for an assertion requiring it to also be true.

$d variables $.

Disjoint variable restriction. For distinct active variables, it forbids the substitution of one variable with another.

label $a constant symbols $.

Axiomatic assertion.

label $p constant symbols $= proof $.

Provable assertion. The proof is a sequence of statement labels. This label sequence serves as a set of instructions that the Metamath program uses to construct a series of math symbol sequences. The construction must ultimately result in the math symbol sequence contained between the $p and $= keywords of the $p statement. For details, see section 4.3 in [1]. Proofs are most easily written using the interactive prompt in metamath.

Files

/usr/share/metamath