`mapDeltaOne`

definition

show as: view math explainer →

module: IndisputableMonolith.RecogSpec.Scales
domain: RecogSpec
line: 167 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.RecogSpec.Scales on GitHub at line 167.

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

 164-- (no actionMap in minimal RSUnits)
 165
 166/-- Specialization of `mapDelta` to δ = 1 using the canonical projection. -/
 167noncomputable def mapDeltaOne
 168  (toZ : LedgerUnits.DeltaSub 1 → ℤ) (f : AffineMapZ) : LedgerUnits.DeltaSub 1 → ℝ :=
 169  fun p => f.slope * ((toZ p) : ℝ) + f.offset
 170
 171@[simp] lemma mapDeltaOne_fromZ_one
 172  (f : AffineMapZ) (n : ℤ) :
 173  mapDeltaOne LedgerUnits.toZ_one f (LedgerUnits.fromZ_one n)
 174    = f.slope * (n : ℝ) + f.offset := by
 175  simp [mapDeltaOne, LedgerUnits.toZ_one, LedgerUnits.fromZ_one]
 176
 177lemma mapDeltaOne_step (f : AffineMapZ) (n : ℤ) :
 178  mapDeltaOne LedgerUnits.toZ_one f (LedgerUnits.fromZ_one (n+1))
 179    - mapDeltaOne LedgerUnits.toZ_one f (LedgerUnits.fromZ_one n) = f.slope := by
 180  simp [mapDeltaOne, add_comm, add_left_comm, add_assoc, sub_eq_add_neg, mul_add]
 181
 182@[simp] lemma mapDeltaTime_fromZ_one
 183  (U : Constants.RSUnits) (n : ℤ) :
 184  mapDeltaOne LedgerUnits.toZ_one (timeMap U) (LedgerUnits.fromZ_one n)
 185    = U.tau0 * (n : ℝ) := by
 186  simp [mapDeltaOne, timeMap, add_comm]
 187
 188-- (no actionMap in minimal RSUnits)
 189
 190end Scales
 191
 192end RecogSpec
 193end IndisputableMonolith

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.