76 lines
3.2 KiB
Plaintext
76 lines
3.2 KiB
Plaintext
section \<open> Physical Constants \<close>
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theory SI_Constants
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imports SI_Proof
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begin
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subsection \<open> Core Derived Units \<close>
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abbreviation "hertz \<equiv> second\<^sup>-\<^sup>\<one>"
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abbreviation "radian \<equiv> meter \<^bold>\<cdot> meter\<^sup>-\<^sup>\<one>"
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abbreviation "steradian \<equiv> meter\<^sup>\<two> \<^bold>\<cdot> meter\<^sup>-\<^sup>\<two>"
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abbreviation "joule \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two>"
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abbreviation "watt \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<three>"
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abbreviation "coulomb \<equiv> ampere \<^bold>\<cdot> second"
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abbreviation "lumen \<equiv> candela \<^bold>\<cdot> steradian"
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subsection \<open> Constants \<close>
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text \<open> The most general types we support must form a field into which the natural numbers can
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be injected. \<close>
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default_sort field_char_0
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text \<open> Hyperfine transition frequency of frequency of Cs \<close>
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abbreviation caesium_frequency:: "'a[T\<^sup>-\<^sup>1]" ("\<Delta>v\<^sub>C\<^sub>s") where
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"caesium_frequency \<equiv> 9192631770 \<odot> hertz"
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text \<open> Speed of light in vacuum \<close>
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abbreviation speed_of_light :: "'a[L \<cdot> T\<^sup>-\<^sup>1]" ("\<^bold>c") where
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"speed_of_light \<equiv> 299792458 \<odot> (meter\<^bold>\<cdot>second\<^sup>-\<^sup>\<one>)"
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text \<open> Planck constant \<close>
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abbreviation Planck :: "'a[M \<cdot> L\<^sup>2 \<cdot> T\<^sup>-\<^sup>2 \<cdot> T]" ("\<^bold>h") where
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"Planck \<equiv> (6.62607015 \<cdot> 1/(10^34)) \<odot> (joule\<^bold>\<cdot>second)"
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text \<open> Elementary charge \<close>
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abbreviation elementary_charge :: "'a[I \<cdot> T]" ("\<^bold>e") where
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"elementary_charge \<equiv> (1.602176634 \<cdot> 1/(10^19)) \<odot> coulomb"
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abbreviation Boltzmann :: "'a[M \<cdot> L\<^sup>2 \<cdot> T\<^sup>-\<^sup>2 \<cdot> \<Theta>\<^sup>-\<^sup>1]" ("\<^bold>k") where
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"Boltzmann \<equiv> (1.380649\<cdot>1/(10^23)) \<odot> (joule \<^bold>/ kelvin)"
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abbreviation Avogadro :: "'a[N\<^sup>-\<^sup>1]" ("N\<^sub>A") where
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"Avogadro \<equiv> 6.02214076\<cdot>(10^23) \<odot> (mole\<^sup>-\<^sup>\<one>)"
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abbreviation max_luminous_frequency :: "'a[T\<^sup>-\<^sup>1]" where
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"max_luminous_frequency \<equiv> (540\<cdot>10^12) \<odot> hertz"
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abbreviation luminous_efficacy :: "'a[J \<cdot> (L\<^sup>2 \<cdot> L\<^sup>-\<^sup>2) \<cdot> (M \<cdot> L\<^sup>2 \<cdot> T\<^sup>-\<^sup>3)\<^sup>-\<^sup>1]" ("K\<^sub>c\<^sub>d") where
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"luminous_efficacy \<equiv> 683 \<odot> (lumen\<^bold>/watt)"
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theorem second_definition:
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"1 \<odot> second \<cong>\<^sub>Q (9192631770 \<odot> \<one>) \<^bold>/ \<Delta>v\<^sub>C\<^sub>s"
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by si_calc
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theorem meter_definition:
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"1 \<odot> meter \<cong>\<^sub>Q (\<^bold>c \<^bold>/ (299792458 \<odot> \<one>))\<^bold>\<cdot>second"
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"1 \<odot> meter \<cong>\<^sub>Q (9192631770 / 299792458) \<odot> (\<^bold>c \<^bold>/ \<Delta>v\<^sub>C\<^sub>s)"
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by si_calc+
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abbreviation gravitational_constant :: "'a[L\<^sup>3 \<cdot> M\<^sup>-\<^sup>1 \<cdot> T\<^sup>-\<^sup>2]" where
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"gravitational_constant \<equiv> (6.6743015 \<cdot> 1/(10 ^ 11)) \<odot> (meter\<^sup>\<three>\<^bold>\<cdot>kilogram\<^sup>-\<^sup>\<one>\<^bold>\<cdot>second\<^sup>-\<^sup>\<two>)"
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default_sort type
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end |