45 lines
1.1 KiB
Plaintext
45 lines
1.1 KiB
Plaintext
section \<open> Imperial Units via SI-Units\<close>
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theory SI_Imperial
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imports SI_Accepted
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begin
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subsection \<open> Definition \<close>
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default_sort field_char_0
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definition degrees_farenheit :: "'a \<Rightarrow> 'a[\<Theta>]" ("_\<degree>F" [999] 999)
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where [si_eq]: "degrees_farenheit x = (x + 459.67)\<cdot>5/9 \<odot> kelvin"
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definition pint :: "'a[Volume]" where
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[si_def, si_eq]: "pint = 0.56826125 \<odot> litre"
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definition inch :: "'a[L]" where
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[si_def, si_eq]: "inch = 25.5 \<odot> milli \<odot> meter"
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definition foot :: "'a[L]" where
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[si_def, si_eq]: "foot = 0.3048 \<odot> meter"
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definition yard :: "'a[L]" where
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[si_def, si_eq]: "yard = 0.9144 \<odot> meter"
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definition mile :: "'a[L]" where
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[si_def, si_eq]: "mile = 1609.344 \<odot> meter"
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default_sort type
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subsection \<open> Properties \<close>
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lemma miles_to_yards: "mile = 1760 \<odot> yard"
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by si_simp
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lemma miles_to_feet: "mile = 5280 \<odot> foot"
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by si_simp
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lemma mph_to_kmh: "1 \<odot> (mile \<^bold>/ hour) = 1.609344 \<odot> ((kilo \<odot> meter) \<^bold>/ hour)"
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by si_simp
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lemma celcius_to_farenheit: "(T::rat)\<degree>C = ((T - 32) \<cdot> 5/9)\<degree>F"
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oops
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end |