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def below_lt

bend-collections-laws-crypto@1.0.0.0 · proofs/math/random/below.bend:125

import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/below.bend as Below
import Base
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend as SRC
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64m128.bend as M128

125# THEOREM: the bounded draw from any source is below n > 0
126def below_lt(~S: Data, ~next: S -> WU.U64 & S, +f: Nat, +n: Nat, +s: S, +hn: {Nat.is_lt(0n, n) == True{} : Bool}) -> {Nat.is_lt(pfst(S, SR.below(~S, ~next, f, n, s)), n) == True{} : Bool}:
127  go_lt(~S, ~next, f, n, SR.draw(64n, SW.value(SRC.fst64(S, next(s))), n), SW.value(SRC.fst64(S, next(s))), SRC.snd64(S, next(s)), M128.fit64(SRC.fst64(S, next(s))), hn, {==})

Uses (13)

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