def div_one

bendtorch-core@0.1.0.0 · src/tensor/matrix_index_proof.bend:93

import Base
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion

93def div_one(+number: Nat) -> {Nat.div(number, 1n) == number : Nat}:
94  %Equal.trans(Nat, Nat.add(Nat.mul(number, 1n), 0n), Nat.mul(number, 1n), number,
95    Conversion.add_zero(Nat.mul(number, 1n)), Nats.mul_one_right(number)) : {Nat.div(_, 1n) == number : Nat}
96  Equal.cong(Nat & Nat, Nat, pair => Pair.fst(Nat, Nat, pair), Nat.divmod(Nat.add(Nat.mul(number, 1n), 0n), 1n), (number, 0n),
97    Equal.sym(Nat & Nat, (number, 0n), Nat.divmod(Nat.add(Nat.mul(number, 1n), 0n), 1n), Nats.divmod_exact(number, 1n, 0n, Unit{})))