Theorem cvmsrcl

Description: Reverse closure for an even covering. (Contributed by Mario Carneiro, 11-Feb-2015)

	Ref	Expression
Hypothesis	cvmcov.1	|- S = ( k e. J |-> { s e. ( ~P C \ { (/) } ) | ( U. s = ( `' F " k ) /\ A. u e. s ( A. v e. ( s \ { u } ) ( u i^i v ) = (/) /\ ( F |` u ) e. ( ( C |`t u ) Homeo ( J |`t k ) ) ) ) } )
Assertion	cvmsrcl	|- ( T e. ( S ` U ) -> U e. J )

Proof

Step	Hyp	Ref	Expression
1		cvmcov.1	|- S = ( k e. J |-> { s e. ( ~P C \ { (/) } ) | ( U. s = ( `' F " k ) /\ A. u e. s ( A. v e. ( s \ { u } ) ( u i^i v ) = (/) /\ ( F |` u ) e. ( ( C |`t u ) Homeo ( J |`t k ) ) ) ) } )
2	1	dmmptss	|- dom S C_ J
3		elfvdm	|- ( T e. ( S ` U ) -> U e. dom S )
4	2 3	sselid	|- ( T e. ( S ` U ) -> U e. J )