tautLib.TAUT

STRUCTURE

SYNOPSIS

Tautology checker. Proves propositional formulae (and instances of them).

LIBRARY

taut

DESCRIPTION

Given an instance of a valid propositional formula, TAUT_PROVE returns the instance of the formula as a theorem. A propositional formula is a term containing only Boolean constants, Boolean-valued variables, Boolean equalities, implications, conjunctions, disjunctions, negations and Boolean-valued conditionals. An instance of a formula is the formula with one or more of the variables replaced by terms of the same type. The conversion accepts terms with or without universal quantifiers for the variables.

FAILURE

Fails if the term is not an instance of a propositional formula or if the instance is not a valid formula.

EXAMPLE

#TAUT_PROVE
# ``!x n y. ((((n = 1) \/ ~x) ==> y) /\ (y ==> ~(n < 0)) /\ (n < 0)) ==> x``;
|- !x n y. ((n = 1) \/ ~x ==> y) /\ (y ==> ~n < 0) /\ n < 0 ==> x

#TAUT_PROVE ``((((n = 1) \/ ~x) ==> y) /\ (y ==> ~(n < 0)) /\ (n < 0)) ==> x``;
|- ((n = 1) \/ ~x ==> y) /\ (y ==> ~n < 0) /\ n < 0 ==> x

#TAUT_PROVE ``!n. (n < 0) \/ (n = 0)``;
Uncaught exception:
HOL_ERR

SEEALSO

TAUT_CONV, TAUT_TAC, PTAUT_PROVE