Lemma 5. For synchronous languages L and K, all of the following hold:
Lemma 5. 3.1. Let K be a perfectoid field extension of Qcyc.
1. Let n : Z×p → &K× be a weight with n ≡ 1 mod p. Then the Xxxxxxxxxx series En is a modular form in M +(0) that satisfies En ≡ 1 mod p inside &K[[q]].
2. Let n1, n2 : Z×p → &× be two weights with n1 ≡ n2 mod p. Let n := n2 · n1−1 be their ratio. Then for any n ∈ Z≥0, multiplication with En induces an isomorphism + En· : Mn1,Γ0(pn) +
Lemma 5. 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.
Lemma 5. For i = 1, 2, wi is strictly convex and bi is strictly concave.
Lemma 5. For every l ∈ R, | | xxx xx(cosh 2g(lt−α))1/2 = l . t→0
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.
Lemma 5. For M a nonzero integer multiple of 2r, we have 2r 2r νM ≤ M + ν2r M .
Lemma 5. 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.
Lemma 5. Define f (ω) : H → R by (5.2) and assume λn > 0. Under Assumptions 4.1-
Lemma 5. For the case of specialized export suppliers, the disagreement payoffs have the properties:
