Documentation

Marginis.CoquandSpitters2012

A constructive proof of Simpson’s Rule #

by THIERRY COQUAND BAS SPITTERS

In the paper, uniform continuity is discussed.

We define it in a concrete setting here, and prove formally that:

def is_limit (a : ) (L : ) (f : ) :
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    noncomputable def is_limit_bool (a : ) (f : ) (L : ) :
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          theorem extraabs (a : ) (h : 0 < a) :
          1 |1 + a|
          theorem (δ : ) (hδ : 0 < δ) :
          1 |δ * δ⁻¹ + δ ^ 2 * (1 / 4)|
          theorem transition (x : ) (y : ) (ha : 0 x) (hb : 0 < y) :
          x < y x ^ 2 < y ^ 2
          def is_uniformly_continuous_on (S : Set ) (f : S) :
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            def is_uniformly_continuous_on' (R : Set ) (S : Set ) (h : R S) (f : S) :
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              theorem uniformlyContOnSq {univ : Set } {h : Set.Icc 0 1 univ} :
              is_uniformly_continuous_on' (Set.Icc 0 1) univ h fun (x : univ) => x ^ 2