Indeed, assuming that there is ( x, y ) with x ≠ y ≠ c such that P x ( x, y ) = P y ( x, y ) = 0, we can deduce a contradiction.
Indeed, assuming that the DS is under conditions of tripping operations and internal axial force F z (s) does not achieve the critical value.
The first implication in (C9) is a consequence of (69) while the second follows applying Theorem 12 with α = 0. Indeed, assuming that | μ | ( B ϱ ) ≲ ϱ n - 1 implies that M 1 is locally bounded, and therefore so is M 0, R # ( D u ) ≡ M R # ( D u ).
You prefer salvation to $1, and prefer $1 to nothing; but there is no such gamble that rewards you with salvation if you win, and nothing if you lose, that you value at $1. Indeed, assuming that the probability of winning remains positive, you prefer the gamble to any finite reward; but if the probability of winning drops to 0, your preference discontinuously switches to the finite reward.
And indeed, assuming that either García or Ramirez-Rosa emerges as the Democratic nominee ― an outcome that is all but certain ― the district's progressive activists are assured a reliable fighter in Washington.
Bringing this double act into the HBO equation in some way, given where Meereen finds itself at the end of season five, could be very interesting indeed – assuming that Asher hangs around, that is, as it's his current intention to travel back to the home of his house, Ironrath, a stronghold positioned north of Winterfell.
The vast majority of observers would indeed assume that smooth, astute, urbane Clooney really is the right man to be the smooth, astute urbane Grant.
Indeed, assume that (4.3) is true.
Indeed, assume that is a subsequence of such that.
Indeed, assume that is not a KKM mapping.
Indeed, assume that is not a KKM mapping; then there exist, with and such that (3.15) .
