1\DOC PRUNE_SOME_RIGHT_RULE 2 3\TYPE {PRUNE_SOME_RIGHT_RULE : (string list -> thm -> thm)} 4 5\SYNOPSIS 6Prunes several hidden variables. 7 8\LIBRARY unwind 9 10\DESCRIBE 11{PRUNE_SOME_RIGHT_RULE [`li1`;...;`lik`]} behaves as follows: 12{ 13 A |- !z1 ... zr. 14 t = ?l1 ... lr. t1 /\ ... /\ eqni1 /\ ... /\ eqnik /\ ... /\ tp 15 ----------------------------------------------------------------------- 16 A |- !z1 ... zr. t = ?li(k+1) ... lir. t1 /\ ... /\ tp 17} 18where for {1 <= j <= k}, each {eqnij} has the form: 19{ 20 "!y1 ... ym. lij x1 ... xn = b" 21} 22and {lij} does not appear free in any of the other conjuncts or in 23{b}. The {li}'s are related by the equation: 24{ 25 {{li1,...,lik}} u {{li(k+1),...,lir}} = {{l1,...,lr}} 26} 27The rule works if one or more of the {eqnij}'s are not present, that 28is if {lij} is not free in any of the conjuncts, but does not work if {lij} 29appears free in more than one of the conjuncts. {p} may be zero, that is, all 30the conjuncts may be {eqnij}'s. In this case the conjunction will be 31transformed to {T} (true). Also, for each {eqnij}, {m} and {n} may be zero. 32 33If there is more than one line with a specified name (but with different 34types), the one that appears outermost in the existential quantifications is 35pruned. If such a line name is mentioned twice in the list, the two outermost 36occurrences of lines with that name will be pruned, and so on. 37 38\FAILURE 39Fails if the argument theorem is not of the specified form or if any of the 40{lij}'s are free in more than one of the conjuncts or if the equation for any 41{lij} is recursive. The function also fails if any of the specified lines are 42not one of the existentially quantified lines. 43 44\EXAMPLE 45{ 46#PRUNE_SOME_RIGHT_RULE [`l1`;`l2`] 47# (ASSUME 48# "!(in:num->bool) (out:num->bool). 49# DEV (in,out) = 50# ?(l1:num->bool) l2. 51# (!x. l1 x = F) /\ (!x. l2 x = ~(in x)) /\ (!x. out x = ~(in x))");; 52. |- !in out. DEV(in,out) = (!x. out x = ~in x) 53} 54\SEEALSO 55unwindLib.PRUNE_RIGHT_RULE, unwindLib.PRUNE_ONCE_CONV, 56unwindLib.PRUNE_ONE_CONV, unwindLib.PRUNE_SOME_CONV, unwindLib.PRUNE_CONV. 57 58\ENDDOC 59