Lemma 5. .18. For synchronous languages L and K, all of the following hold:
Lemma 5. .14. There is an absolute upper bound c, independent of the input Z0, on the number of iterations of Algorithm 5.9 in which Z sat- isfies y1 ≥ 1 at the beginning of step 3. C ≥
Lemma 5. .4. For i = 1, 2, wi is strictly convex and bi is strictly concave.
Lemma 5. 1.4. For every l ∈ R, | | xxx xx(cosh 2g(lt−α))1/2 = l . t→0
Lemma 5. 2.1. Define f (ω) : H → R by (5.2) and assume λn > 0. Under Assumptions 4.1-
Lemma 5. 3.1. Let K be a perfectoid field extension of Qcyc.
Lemma 5. 4.2. Enb is the q-expansion of a unique t-adic overconvergent modular form of weight nb and radius of overconvergence ϵnb as defined in Definition 3.3.6.
Lemma 5. For M a nonzero integer multiple of 2r, we have r,c 2r r,c 2r νM ≤ M + ν2r M . r,c
Lemma 5. For the case of specialized export suppliers, the disagreement payoffs have the properties: 6W m(t m) –23t m–3x+(26 –23)y
Lemma 5. If, at time 3∆, an honest party receives at least N sets of signatures which are all consistent with (the same) x, no honest party receives a set of signatures that is weakly consistent with x′ x.
