Proof.pascal: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend as Proof
Lines 97-100 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&start_line=97&end_line=100

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

def pascal(+m: Nat, +j: Nat) -> S.Comb.pascal(m, j):
  %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}
  %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}
  F.comb_ok(1n+m, 1n+j)

Uses (7):
  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.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend&name=comb_ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=Comb.pascal
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=choose
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=comb