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  2. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    The proof is written as a series of lines in two columns. In each line, the left-hand column contains a proposition, while the right-hand column contains a brief explanation of how the corresponding proposition in the left-hand column is either an axiom, a hypothesis, or can be logically derived from previous propositions.

  3. Direct proof - Wikipedia

    en.wikipedia.org/wiki/Direct_proof

    In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established facts, usually axioms, existing lemmas and theorems, without making any further assumptions. [1]

  4. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.

  5. Method of analytic tableaux - Wikipedia

    en.wikipedia.org/wiki/Method_of_analytic_tableaux

    A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]

  6. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol. Basic logic symbols [ edit ]

  7. Proof procedure - Wikipedia

    en.wikipedia.org/wiki/Proof_procedure

    A proof procedure for a logic is complete if it produces a proof for each provable statement. The theorems of logical systems are typically recursively enumerable, which implies the existence of a complete but usually extremely inefficient proof procedure; however, a proof procedure is only of interest if it is reasonably efficient.

  8. Suppes–Lemmon notation - Wikipedia

    en.wikipedia.org/wiki/Suppes–Lemmon_notation

    1965: The entire textbook by Lemmon (1965) is an introduction to logic proofs using a method based on that of Suppes. 1967: In a textbook, Kleene (2002 , pp. 50–58, 128–130) briefly demonstrated two kinds of practical logic proofs, one system using explicit quotations of antecedent propositions on the left of each line, the other system ...

  9. List of long mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_long_mathematical...

    Hejhal's proof of a general form of the Selberg trace formula consisted of 2 volumes with a total length of 1322 pages. Arthur–Selberg trace formula. Arthur's proofs of the various versions of this cover several hundred pages spread over many papers. 2000 Almgren's regularity theorem. Almgren's proof was 955 pages long.