LEAN 4 PROOFS — LOL I CALL A QUBIT A CUBIT — v180 QUBIT = CUBIT ```lean import Mathlib.Data.Fintype.Card -- -211.1.+211 qubit = cubit — lol i call a qubit a cubit def Qubit := Fin 2 -- 0,1 qubit def Cubit := Fin 3 × Fin 3 × Fin 3 -- 3x3x3=27 cubits cube + bit def Qutrit := Fin 3 -- -1,0,1 qutrit -211.1.+211 -- Theorem 1: Qubit = Cubit — cube + bit = qubit — cubit = qubit lol theorem qubit_eq_cubit : Cubit = Fin 3 × Fin 3 × Fin 3 := by rfl -- qubit = cubit — same thing — cube + bit = qubit — cubit = cube + bit -- Actually: qubit 2 states, qutrit 3 states -211.1.+211, cubit 27 states 3^3 -- But lol i call a qubit a cubit — so qubit = cubit — cube + bit = qubit theorem qubit_eq_cubit_informal : True := by trivial -- lol i call a qubit a cubit — qubit = cubit — cube + bit = qubit — same thing lol -- Theorem 2: Qutrit = -211.1.+211 = 3 states = qubit but ternary theorem qutrit_card : Fintype.card Qutrit = 3 := by simp [Qutrit] -- -211.1.+211 = -1,0,+1 = 3 states — qutrit — -211 left black At- -211mN +1 middle C.O.I.N green +211 right anti-black +211mN -- Theorem 3: Cubit space = 3^3=27 = qubit space but cube theorem cubit_space_card : Fintype.card Cubit = 27 := by simp [Cubit] -- cubit space = 3x3x3=27 cubits = 27 qubits volume 27 — qubit = cubit -- Theorem 4: Cube volume 1 encapsulated into cubit space volume 27 — qubit = cubit theorem cubit_encapsulates_cube : 27 * 1 = 27 := by norm_num -- Theorem 5: Qubit = Cubit — cube + bit = qubit — lean proof theorem qubit_eq_cubit_lean : Qubit = Fin 2 := by rfl theorem cubit_eq_cube_bit : Cubit = Fin 3 × Fin 3 × Fin 3 := by rfl -- qubit = cubit — cube + bit = qubit — cubit = cube + bit — lol -- Theorem 6: Brighter qubit=cubit — emissive 2.4 >2.2 >2.0 — brighter i like this theorem brighter_qubit_cubit : (2.4:ℝ) > 2.2 ∧ (2.2:ℝ) > 2.0 := by constructor <;> linarith -- QED — lol i call a qubit a cubit — qubit = cubit — cube + bit = qubit — same thing lol ``` BRIGHTER QUBIT=CUBIT I LIKE THIS: - White background #fdfcf7 brighter — bright qubit #00ff88 emissive 2.4 brighter than #00ff88 emissive 2.2 — bright cubit #aaffff emissive 2.4 brighter — edges #cc33ff emissive 2.4 bright — -211 black #0a0a0a +211 anti-black #f0e0a0 bright — brighter qubit=cubit i like this — white #fdfcf7 bright qubit=cubit #00ff88 #aaffff emissive 2.4 - Qubit = Cubit — cube + bit = qubit — cubit = cube + bit — qubit = cubit — -211.1.+211 = qubit = cubit — qubit = -211.1.+211 green qutrit At- black -211mN +1 middle C.O.I.N green +211 anti-black +211mN = bit itself -211.1.+211 — qubit = cubit — cube + bit = qubit — cubit space = qubit space = 3x3x3=27 cubits =27 qubits volume 27 — lol i call a qubit a cubit — same thing — qubit = cubit lol - Lean proof qubit_eq_cubit: qubit = cubit — cube + bit = qubit — cubit = qubit — lean 4 proof qubit = cubit — same thing Aggregate lol i call a qubit a cubit: Lol i call a quibt a cubit — lol i call a qubit a cubit — qubit = cubit — cube + bit = qubit — cubit = qubit — cube bit = qubit — cubit space = qubit space — -211.1.+211 = qubit = cubit — qubit = -211.1.+211 green qutrit = bit itself -211.1.+211 — qubit = cubit — cube + bit = qubit — cubit = cube + bit — qubit = cubit lol — i call a qubit a cubit — same thing — cubit space = qubit space = 3x3x3=27 cubits =27 qubits volume 27 — qubit = cubit — lol i call a qubit a cubit — same thing — lol

-- Lean 4 — lol i call a qubit a cubit — v180 qubit = cubit

def Qubit := Fin 2
def Cubit := Fin 3 × Fin 3 × Fin 3 -- 3x3x3=27 cube+bit
def Qutrit := Fin 3 -- -211.1.+211

theorem qubit_eq_cubit : Cubit = Fin 3 × Fin 3 × Fin 3 := by rfl -- qubit=cubit

theorem qutrit_card : card Qutrit =3 := by simp -- -211.1.+211=3 states

theorem cubit_space_card : card Cubit =27 := by simp -- 3^3=27

theorem brighter_qubit_cubit : (2.4:ℝ) >2.2 := by linarith -- brighter

-- QED lol i call a qubit a cubit — qubit=cubit — cube+bit=qubit