def pascal

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/proof.bend:97

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend as F

97def pascal(+m: Nat, +j: Nat) -> S.Comb.pascal(m, j):
98  %Equal.sym(Nat, M.comb(m, j), S.choose(m, j), F.comb_ok(m, j)) : {M.comb(1n+m, 1n+j) == Nat.add(_, M.comb(m, 1n+j)) : Nat}
99  %Equal.sym(Nat, M.comb(m, 1n+j), S.choose(m, 1n+j), F.comb_ok(m, 1n+j)) : {M.comb(1n+m, 1n+j) == Nat.add(S.choose(m, j), _) : Nat}
100  F.comb_ok(1n+m, 1n+j)