The capability vrf-lite command will disable provider edge (PE)specific checks on RouterA. PE checks are used to prevent loops when the Open Shortest Path First (OSPF) process on a PE is associated with the VPN routing and forwarding (VRF) instance and the router is mutually redistributing OSPF and Border Gateway Protocol (BGP). VRF enables multiple instances of a routing table to exist on a router. When OSPF is associated with a VRF instance and is being mutually redistributed with BGP, it is possible for routing loops to occur. PE checks examine linkstate advertisements (LSAs) to determine whether a specific path should be considered for insertion into the routing table. However, PE checks are not necessary on a router that is not running BGP and is therefore not a PE router.

The address-family ipv4 vrf command does not disable PE checks. Instead, the address-family ipv4 vrf vrf-name command is used to configure VRF contexts under a routing process. For example, to configure the routing context for VRF kyiv under Enhanced Interior Gateway Routing Protocol (EIGRP) process 65000, you would issue the following commands:
RouterA(config)#router eigrp 65000 RouterA(config-router)#address-family ipv4 vrf kyiv

Neither the ip vrf command nor the ip vrf forwarding command disables PE checks. Instead, the ip vrf forwarding vrfname command adds a VRF instance to an interface.
Fo example, to add the VRF kyiv to the FastEthernet0/1 interface on RouterA, you would issue the following commands:
RouterA(config)#interface FastEthernet0/1 RouterA(config-if)#ip vrf forwarding kyiv