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Proof that the set remove_singleton pair(xset, y) is a subset of xset

----> UNIT CONFLICT at   0.63 sec ----> 138 [binary,136.1,81.1] $F.

Length of proof is 3.  Level of proof is 3.

Proof



1 [reference] k(x) y=x.
2 [reference] p1 pair(x,y)=x.
3 [reference] p2 pair(x,y)=y.
4 [reference] pair(x,y) z=pair(x z,y z).
5 [reference] pair(p1 x,p2 x)=x.
6 [reference] abst x y z=x k(z) (y z).
21 [reference] p1 x=p2 x |eq x =p2.
52 [reference] pair(x1,y1)!=pair(x2,y2)|x1=x2.
79 [reference] remove_singleton=abst k(abst k(eq)) pair(k(k(pair(p1,p2))),pair(p1,abst k(abst k(eq)) pair(p2,k(pair(p1,p2))))).
81 [assumption to refute] badset bad!=p1.
82 [assumption to refute] p.
83 [assumption to refute] -p|remove_singleton pair(badset,bad1) bad !=p2.
102 [ur,83,82,demod,79,6,1,4,1,4,2,6,1,4,3,1,6,1,4,1,4,6,1,4,4,5] eq pair(pair(p1,p2),pair(badset bad,eq pair(bad1 bad,bad)))!=p
2.
112 [hyper,102,21,demod,2,3,flip.1] pair(badset bad,eq pair(bad1 bad,bad))=pair(p1,p2).
136 [hyper,112,52] badset bad=p1.
138 [binary,136.1,81.1] $F.



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