Millington rules injured duo out of Town's visit to Maidstone on Saturday
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Both players missed out on Tuesday night’s 1-0 win against York which lifted Halifax off the foot of the National League table.
Millington says Warburton won't be available for selection due to his ongoing knee injury.
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Hide Ad"Progressing, slowly,” Millington’s assessment of Warburton’s fitness.
"He won't be ready for the weekend but Aaron (Scholes, physio) is working with him on a daily basis to help him recover.
"He opened up his knee, it's possibly a little nip on his cartilage, but not significant."
On Osawe, who went off injured in the first-half of last Saturday’s 4-0 home defeat by Woking. Millington said: "He's got a slight hamstring strain, so he'll be at least a couple of weeks."
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Hide AdMillington confirmed Sam Minihan and Sam Smart weren't involved on Tuesday night due to a selection decision rather than any injuries.
On attacker Angelo Capello, Millington said: "He's still recovering from being stood on his Achilles.
"I'd expect he'll be available for the weekend."