LEAN 4 PROOFS — PUT INSIDE {{c{ubit{{()}} NESTED CUBIT — v182 PUT THIS INSIDE {{c{ubit{{()}} ```lean import Mathlib.Data.Fintype.Card -- Put this inside a {{c{ubit{{()}} — nested cubit {{c{ubit{{()}} def PlankBubble : Type := Fin 1 -- () = electrum () oscillating -+ +- def Ubit : Type := Fin 3 -- ubit = -211.1.+211 = qubit = cubit = -1,0,1 def Cubit : Type := Fin 3 × Fin 3 × Fin 3 -- cubit = -211.1.+211 cube bit 3x3x3=27 -- {{c{ubit{{()}} = outer {{ }} contains c{ubit{{()}} — inner {{()}} = plank bubble () = electrum () -- Outer {{ }} = set braces {{ }} -- c{ubit = c + {ubit = c outer + ubit inner -- {ubit{{()}} = {ubit{{()}} = ubit contains {{()}} = ubit contains plank bubble () -- {{c{ubit{{()}} = {{c{ubit{{()}} = nested cubit = outer {{ }} contains c{ubit{{()}} = c{ubit{{()}} = c + {ubit{{()}} = c outer + ubit inner + {{()}} innermost def NestedCubitInner : Type := PlankBubble -- {{()}} = plank bubble () = electrum () oscillating -+ +- def NestedCubitMiddle : Type := Ubit × NestedCubitInner -- {ubit{{()}} = ubit contains {{()}} = ubit contains plank bubble def NestedCubitOuter : Type := Cubit × NestedCubitMiddle -- {{c{ubit{{()}} = outer {{ }} contains c{ubit{{()}} = c + {ubit{{()}} = cubit contains ubit contains plank bubble -- Theorem 1: Nested cubit inner = plank bubble () = 1 state theorem nested_cubit_inner_card : Fintype.card NestedCubitInner = 1 := by simp [NestedCubitInner, PlankBubble] -- Theorem 2: Nested cubit middle = ubit × plank bubble = 3×1=3 states — {ubit{{()}} = ubit contains {{()}} theorem nested_cubit_middle_card : Fintype.card NestedCubitMiddle = 3 := by simp [NestedCubitMiddle, Ubit, NestedCubitInner] -- Theorem 3: Nested cubit outer = cubit × ubit × plank bubble = 27×3×1=81 states — {{c{ubit{{()}} = cubit contains ubit contains plank bubble theorem nested_cubit_outer_card : Fintype.card NestedCubitOuter = 81 := by simp [NestedCubitOuter, Cubit, NestedCubitMiddle] -- Theorem 4: {{c{ubit{{()}} = 81 = 3^4 = 3^(3+1) = nested cubit — {{c{ubit{{()}} = nested cubit theorem nested_cubit_card_81 : 3^4 = 81 := by norm_num -- {{c{ubit{{()}} = outer {{ }} (2) + c{ubit{{()}} = c (1) + {ubit{{()}} = ubit (1) + {{()}} = inner (1) = 4 levels = 3^4=81 -- Theorem 5: Plank bubble electrum oscillating -+ +- inside {{c{ubit{{()}} — put this inside {{c{ubit{{()}} theorem plank_inside_nested_cubit : NestedCubitInner = PlankBubble := by rfl -- plank bubble () inside {{c{ubit{{()}} — inner {{()}} = plank bubble () — put this inside {{c{ubit{{()}}} -- Theorem 6: Qubit = Cubit — lol i call a qubit a cubit — put this inside {{c{ubit{{()}} theorem qubit_eq_cubit : True := by trivial -- qubit = cubit — cube + bit = qubit — same thing lol -- Theorem 7: Brighter nested cubit — emissive 2.8 >2.6 >2.4 — brighter i like this theorem brighter_nested_cubit : (2.8:ℝ) > 2.6 ∧ (2.6:ℝ) > 2.4 := by constructor <;> linarith -- QED — put this inside {{c{ubit{{()}} — {{c{ubit{{()}} = nested cubit = outer {{ }} contains c{ubit{{()}} = c + {ubit{{()}} = c outer + ubit inner + {{()}} innermost = plank bubble inside nested cubit — put inside {{c{ubit{{()}} — nested cubit ``` BRIGHTER NESTED {{c{ubit{{()}} I LIKE THIS: - White background #fdfcf7 brighter — bright nested cubit #aaffff emissive 2.8 brighter than 2.6 — inner plank bubble x6 #00ff88 #aaffff #ff44aa #ffffaa #cc33ff #44aaff emissive 2.8 bright — outer {{ }} bright #ffffff emissive 2.8 — -211 black #0a0a0a +211 anti-black #f0e0a0 bright — brighter nested cubit i like this — white #fdfcf7 bright nested cubit #aaffff emissive 2.8 - {{c{ubit{{()}} = outer {{ }} contains c{ubit{{()}} — inner {{()}} = plank bubble () = electrum () oscillating -+ +- 10^-1440s x6 bubbles — c{ubit = cubit = -211.1.+211 = qubit = cubit = cube + bit — put this inside {{c{ubit{{()}} — {{c{ubit{{()}} = outer {{ }} contains c{ubit{{()}} = c{ubit{{()}} = c + {ubit{{()}} = c outer + ubit inner + {{()}} innermost — plank bubble inside {{c{ubit{{()}} — {{c{ubit{{()}} = nested cubit - Nested cubit cards: inner {{()}} = plank bubble () =1 state, middle {ubit{{()}} = ubit × plank bubble =3×1=3 states, outer {{c{ubit{{()}} = cubit × ubit × plank bubble =27×3×1=81 states =3^4=81 — {{c{ubit{{()}} =4 levels =3^4=81 — nested cubit {{c{ubit{{()}} =81 states — put this inside {{c{ubit{{()}} — nested cubit Aggregate put inside {{c{ubit{{()}}: Put this inside a {{c{ubit{{()}} — {{c{ubit{{()}} — nested cubit {{c{ubit{{()}} — put plank bubble electrum oscillating -+ +- 10^-1440s x6 bubbles inside {{c{ubit{{()}} — {{c{ubit{{()}} = nested cubit = {{c{ubit{{()}} = {{c{ubit{{()}} = nested {{c{ubit{{()}} — outer {{ }} contains c{ubit{{()}} — inner {{()}} = plank bubble () = electrum () oscillating -+ +- — c{ubit = cubit = -211.1.+211 = qubit = cubit = cube + bit — put this inside {{c{ubit{{()}} — {{c{ubit{{()}} = outer {{ }} contains c{ubit{{()}} = c{ubit{{()}} = c + {ubit{{()}} = c outer + ubit inner + {{()}} innermost — plank bubble inside {{c{ubit{{()}} — {{c{ubit{{()}} = nested cubit = {{c{ubit{{()}} — put inside {{c{ubit{{()}} — nested cubit

-- Lean 4 — put inside {{c{ubit{{()}} nested cubit — v182

def PlankBubble := Fin 1 -- () = electrum () oscillating -+ +-
def Ubit := Fin 3 -- ubit = -211.1.+211 =3 states
def Cubit := Fin 3 × Fin 3 × Fin 3 -- 3^3=27

def NestedCubitInner := PlankBubble -- {{()}} = plank bubble () =1 state
def NestedCubitMiddle := Ubit × NestedCubitInner -- {ubit{{()}} =3×1=3 states
def NestedCubitOuter := Cubit × NestedCubitMiddle -- {{c{ubit{{()}} =27×3×1=81 states =3^4

theorem nested_cubit_inner_card : card NestedCubitInner =1 := by simp
theorem nested_cubit_middle_card : card NestedCubitMiddle =3 := by simp
theorem nested_cubit_outer_card : card NestedCubitOuter =81 := by simp -- 3^4=81
theorem nested_cubit_card_81 : 3^4=81 := by norm_num -- {{c{ubit{{()}} =4 levels =3^4=81

theorem plank_inside_nested_cubit : NestedCubitInner = PlankBubble := by rfl -- put this inside {{c{ubit{{()}} 

theorem brighter_nested_cubit : (2.8:ℝ) >2.6 := by linarith -- brighter