`CalculusTheorem`

definition

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module: IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS
domain: Mathematics
line: 25 · github
papers citing: none yet

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IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS on GitHub at line 25.

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formal source

  22namespace IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS
  23open Cost
  24
  25inductive CalculusTheorem where
  26  | FTC1 | FTC2 | meanValue | intermediateValue | lhopital
  27  deriving DecidableEq, Repr, BEq, Fintype
  28
  29theorem calculusTheoremCount : Fintype.card CalculusTheorem = 5 := by decide
  30
  31/-- J(1) = 0 (minimum, derivative = 0 at critical point). -/
  32theorem jcost_minimum : Jcost 1 = 0 := Jcost_unit0
  33
  34/-- J is positive off minimum (strict local minimum). -/
  35theorem jcost_strict_min {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  36    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  37
  38structure CalculusCert where
  39  five_theorems : Fintype.card CalculusTheorem = 5
  40  minimum_at_1 : Jcost 1 = 0
  41  strict_minimum : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  42
  43def calculusCert : CalculusCert where
  44  five_theorems := calculusTheoremCount
  45  minimum_at_1 := jcost_minimum
  46  strict_minimum := jcost_strict_min
  47
  48end IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS

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