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We show that subpresentations of aspherical prounipotent presentations overfields of zero characteristics and subpresentations of asphericalpro-$p$-presentations are aspherical, an application to subpresentations ofaspherical discrete presentations is also included. Following Bousfield-Kan,Quillen and Sullivan the results are regarded as affirmative answers torational and $p$-adic analogs of J.H.C. Whitehead's conjecture.

Rational and $p$-adic analogs of J.H.C. Whitehead's conjecture