Definitions for words used in this project

atom

• a statement which cannot be broken down into smaller statements.

axiom

• a statement or proposition that is regarded as being established, accepted, or self-evidently true.

complete

• for every statement of a language of the system either the statement or it's negation can be derived.

consistent

• No statement and it's negation are both derivable

postulate

• suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief

derivation

• the obtaining or developing of something from a source or origin.

function

• A mathematical relation such that each element of a given set (domain of the function) is associated with an element of another set ( range of the function)

inference rule

• a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions)
• aka transformation rule

lemma

• a subsidiary or intermediate theorem in an argument or proof.

operator

• a symbol or function representing a mathematical operation

statement

• aka "expression" in Mathematica
• includes equations and inequalities
• has LHS, RHS

theorem

• a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.

terms

• A+B

operators

• +,x

products

• A*B