`half`

proved

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module: IndisputableMonolith.RecogSpec.Core
domain: RecogSpec
line: 111 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.RecogSpec.Core on GitHub at line 111.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

used by

formal source

 108lemma of_nat (φ : ℝ) (n : ℕ) : PhiClosed φ (n : ℝ) := by
 109  simpa using of_rat φ n
 110
 111lemma half (φ : ℝ) : PhiClosed φ (1 / (2 : ℝ)) := by
 112  have htwo : PhiClosed φ ((2 : ℚ) : ℝ) := of_rat φ 2
 113  simpa using inv htwo
 114
 115end PhiClosed
 116
 117/-- Universal φ-closed targets RS claims are forced to take. -/
 118structure UniversalDimless (φ : ℝ) : Type where
 119  alpha0        : ℝ
 120  massRatios0   : LeptonMassRatios
 121  mixingAngles0 : CkmMixingAngles
 122  g2Muon0       : ℝ
 123  strongCP0     : Prop
 124  eightTick0    : Prop
 125  born0         : Prop
 126  alpha0_isPhi        : PhiClosed φ alpha0
 127  massRatios0_isPhi   : massRatios0.Forall (PhiClosed φ)
 128  mixingAngles0_isPhi : mixingAngles0.Forall (PhiClosed φ)
 129  g2Muon0_isPhi       : PhiClosed φ g2Muon0
 130
 131/-- "Bridge B matches universal U" (pure proposition). -/
 132def Matches (φ : ℝ) (L : Ledger) (B : Bridge L) (U : UniversalDimless φ) : Prop :=
 133  ∃ (P : DimlessPack L B),
 134    P.alpha = U.alpha0
 135      ∧ P.massRatios = U.massRatios0
 136      ∧ P.mixingAngles = U.mixingAngles0
 137      ∧ P.g2Muon = U.g2Muon0
 138      ∧ P.strongCPNeutral = U.strongCP0
 139      ∧ P.eightTickMinimal = U.eightTick0
 140      ∧ P.bornRule = U.born0
 141

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