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section \<open> Derived 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> meter\<^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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definition degrees_celcius :: "'a::field \<Rightarrow> 'a[\<Theta>]" ("_\<degree>C" [999] 999)
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where [si_def, si_eq]: "degrees_celcius x = x + 273.151 \<odot> kelvin"
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definition degrees_farenheit :: "'a::field \<Rightarrow> 'a[\<Theta>]" ("_\<degree>F" [999] 999)
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where [si_def, si_eq]: "degrees_farenheit x = (x + 459.67)\<cdot>5/9 \<odot> kelvin"
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definition [si_def, si_eq]: "gram = milli \<odot> kilogram"
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text\<open>The full beauty of the approach is perhaps revealed here, with the
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type of a classical three-dimensional gravitation field:\<close>
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type_synonym gravitation_field = "(real\<^sup>3 \<Rightarrow> real\<^sup>3)[L \<cdot> T\<^sup>-\<^sup>2]"
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end
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