def mod_self
bend-collections-laws-math@1.0.0.0 · proofs/math/natural/inverse.bend:136
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend as Inverse
import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend as LC
136def mod_self(+mp: Nat) -> {Nat.mod(1n+mp, 1n+mp) == 0n : Nat}:
137 %Equal.sym(Nat, 1n+mp, Nat.add(Nat.mul(1n, 1n+mp), 0n), Equal.trans(Nat, 1n+mp, Nat.mul(1n, 1n+mp), Nat.add(Nat.mul(1n, 1n+mp), 0n), Equal.sym(Nat, Nat.mul(1n, 1n+mp), 1n+mp, LC.one_mul(1n+mp)), Equal.sym(Nat, Nat.add(Nat.mul(1n, 1n+mp), 0n), Nat.mul(1n, 1n+mp), A.add_zero(Nat.mul(1n, 1n+mp))))) : {Nat.mod(_, 1n+mp) == 0n : Nat}
138 R.mod_of(1n, mp, 0n, {==})