def sel_lt

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/scalar2.bend:114

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

114def 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}:
115  match b:
116    case 0n:
117      {==}
118    case 1n:
119      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)
120    case 2n+q:
121      Empty.absurd({Nat.is_lt(Nat.mul(2n+q, S), 1n+mm) == True{} : Bool}, L.false_true(hb))