Scalar2.sel_lt: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend as Scalar2
Lines 114-121 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar2.bend&start_line=114&end_line=121

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as AR

def sel_lt(+mm: Nat, +b: Nat, +S: Nat, +hb: {Nat.is_le(b, 1n) == True{} : Bool}, +ls: {Nat.is_lt(S, 1n+mm) == True{} : Bool}) -> {Nat.is_lt(Nat.mul(b, S), 1n+mm) == True{} : Bool}:
  match b:
    case 0n:
      {==}
    case 1n:
      L.subst(Nat, z => {Nat.is_lt(z, 1n+mm) == True{} : Bool}, S, Nat.mul(1n, S), Equal.sym(Nat, Nat.mul(1n, S), S, AR.one_mul(S)), ls)
    case 2n+q:
      Empty.absurd({Nat.is_lt(Nat.mul(2n+q, S), 1n+mm) == True{} : Bool}, L.false_true(hb))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&name=one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst