88 lines
3.4 KiB
Plaintext
Executable File
88 lines
3.4 KiB
Plaintext
Executable File
section \<open> Derived SI-Units\<close>
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theory SI_Derived
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imports SI_Prefix
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begin
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subsection \<open> Definitions \<close>
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abbreviation "newton \<equiv> kilogram \<^bold>\<cdot> meter \<^bold>\<cdot> second\<^sup>-\<^sup>\<two>"
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abbreviation "pascal \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>-\<^sup>\<one> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two>"
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abbreviation "volt \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<three> \<^bold>\<cdot> ampere\<^sup>-\<^sup>\<one>"
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abbreviation "farad \<equiv> kilogram\<^sup>-\<^sup>\<one> \<^bold>\<cdot> meter\<^sup>-\<^sup>\<two> \<^bold>\<cdot> second\<^sup>\<four> \<^bold>\<cdot> ampere\<^sup>\<two>"
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abbreviation "ohm \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<three> \<^bold>\<cdot> ampere\<^sup>-\<^sup>\<two>"
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abbreviation "siemens \<equiv> kilogram\<^sup>-\<^sup>\<one> \<^bold>\<cdot> meter\<^sup>-\<^sup>\<two> \<^bold>\<cdot> second\<^sup>\<three> \<^bold>\<cdot> ampere\<^sup>\<two>"
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abbreviation "weber \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two> \<^bold>\<cdot> ampere\<^sup>-\<^sup>\<one>"
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abbreviation "tesla \<equiv> kilogram \<^bold>\<cdot> second\<^sup>-\<^sup>\<two> \<^bold>\<cdot> ampere\<^sup>-\<^sup>\<one>"
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abbreviation "henry \<equiv> kilogram \<^bold>\<cdot> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two> \<^bold>\<cdot> ampere\<^sup>-\<^sup>\<two>"
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abbreviation "lux \<equiv> candela \<^bold>\<cdot> steradian \<^bold>\<cdot> meter\<^sup>-\<^sup>\<two>"
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abbreviation (input) "becquerel \<equiv> second\<^sup>-\<^sup>\<one>"
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abbreviation "gray \<equiv> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two>"
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abbreviation "sievert \<equiv> meter\<^sup>\<two> \<^bold>\<cdot> second\<^sup>-\<^sup>\<two>"
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abbreviation "katal \<equiv> mole \<^bold>\<cdot> second\<^sup>-\<^sup>\<one>"
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definition degrees_celcius :: "'a::field_char_0 \<Rightarrow> 'a[\<Theta>]" ("_\<degree>C" [999] 999)
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where [si_eq]: "degrees_celcius x = (x \<odot> kelvin) + approx_ice_point"
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definition [si_eq]: "gram = milli \<odot> kilogram"
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subsection \<open> Equivalences \<close>
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lemma joule_alt_def: "joule \<cong>\<^sub>Q newton \<^bold>\<cdot> meter"
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by si_calc
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lemma watt_alt_def: "watt \<cong>\<^sub>Q joule \<^bold>/ second"
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by si_calc
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lemma volt_alt_def: "volt = watt \<^bold>/ ampere"
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by simp
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lemma farad_alt_def: "farad \<cong>\<^sub>Q coulomb \<^bold>/ volt"
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by si_calc
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lemma ohm_alt_def: "ohm \<cong>\<^sub>Q volt \<^bold>/ ampere"
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by si_calc
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lemma siemens_alt_def: "siemens \<cong>\<^sub>Q ampere \<^bold>/ volt"
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by si_calc
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lemma weber_alt_def: "weber \<cong>\<^sub>Q volt \<^bold>\<cdot> second"
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by si_calc
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lemma tesla_alt_def: "tesla \<cong>\<^sub>Q weber \<^bold>/ meter\<^sup>\<two>"
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by si_calc
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lemma henry_alt_def: "henry \<cong>\<^sub>Q weber \<^bold>/ ampere"
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by si_calc
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lemma lux_alt_def: "lux = lumen \<^bold>/ meter\<^sup>\<two>"
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by simp
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lemma gray_alt_def: "gray \<cong>\<^sub>Q joule \<^bold>/ kilogram"
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by si_calc
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lemma sievert_alt_def: "sievert \<cong>\<^sub>Q joule \<^bold>/ kilogram"
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by si_calc
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subsection \<open> Properties \<close>
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lemma kilogram: "kilo \<odot> gram = kilogram"
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by (si_simp)
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lemma celcius_to_kelvin: "T\<degree>C = (T \<odot> kelvin) + (273.15 \<odot> kelvin)"
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by (si_simp)
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end |