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LEFT_PBETA                                                 (PairRules)
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LEFT_PBETA : (thm -> thm)

KEYWORDS
rule.

LIBRARY
pair

SYNOPSIS
Beta-reduces a top-level paired beta-redex on the left-hand side of an equation.

DESCRIBE
When applied to an equational theorem, {LEFT_PBETA} applies paired
beta-reduction at top level to the left-hand side (only).
Variables are renamed if necessary to avoid free variable capture.

    A |- (\x. t1) t2 = s
   ----------------------  LEFT_PBETA
     A |- t1[t2/x] = s




FAILURE
Fails unless the theorem is equational, with its left-hand side being
a top-level paired beta-redex.

SEEALSO
Drule.RIGHT_BETA, PairRules.PBETA_CONV, PairRules.PBETA_RULE,
PairRules.PBETA_TAC, PairRules.RIGHT_PBETA,
PairRules.RIGHT_LIST_PBETA, PairRules.LEFT_LIST_PBETA.

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