let T, T' be Tree; :: thesis: for p being FinSequence of NAT st p in Leaves T holds
T c= T with-replacement p,T'
let p be FinSequence of NAT ; :: thesis: ( p in Leaves T implies T c= T with-replacement p,T' )
assume A1: p in Leaves T ; :: thesis: T c= T with-replacement p,T'
let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in T or x in T with-replacement p,T' )
assume x in T ; :: thesis: x in T with-replacement p,T'
then reconsider t = x as Element of T ;
( not p is_a_proper_prefix_of t & p in T ) by A1, TREES_1:def 8;
hence x in T with-replacement p,T' by TREES_1:def 12; :: thesis: verum