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polishing.

This commit is contained in:
Burkhart Wolff 2020-02-24 18:47:51 +01:00
parent 493a6c5559
commit f505e6cb79
2 changed files with 14 additions and 9 deletions
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21
src/SI/SI_Units.thy
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@ -4,7 +4,7 @@ theory SI_Units
imports SI_Dimensions
begin
section \<open> The semantic SI-\<^theory_text>\<open>Unit\<close>-Type and its Operations \<close>
section \<open> The Semantic SI-Unit-Type and its Operations \<close>
record 'a Unit =
mag :: 'a \<comment> \<open> Magnitude of the unit \<close>
@ -94,7 +94,7 @@ end
instance Unit_ext :: (order, order) order
by (intro_classes, auto simp add: less_Unit_ext_def less_eq_Unit_ext_def)
section \<open> The abstract SI-\<^theory_text>\<open>Unit\<close>-type and its Operations \<close>
section \<open> The Abstract SI-\<^theory_text>\<open>Unit\<close>-Type and its Operations \<close>
text\<open>We 'lift' SI type expressions to SI unit type expressions as follows:\<close>
@ -111,17 +111,22 @@ definition coerceUnit :: "'u\<^sub>2 itself \<Rightarrow> 'a['u\<^sub>1::dim_typ
subsection\<open>Predicates on Abstract SI-\<^theory_text>\<open>Unit\<close>-types\<close>
text \<open> Two SI Unit types are equivalent if they have the same dimensions
(not necessarily dimension types). This is the whole point of the construction. \<close>
text \<open> Two SI Unit types are orderable if their magnitude type is of class @{class "order"},
and have the same dimensions (not necessarily dimension types).\<close>
lift_definition qless_eq ::
"'n::order['a::dim_type] \<Rightarrow> 'n['b::dim_type] \<Rightarrow> bool" (infix "\<lesssim>\<^sub>Q" 50) is "(\<le>)" .
lift_definition qequiv ::
text\<open> Two SI Unit types are equivalent if they have the same dimensions
(not necessarily dimension types). This equivalence the a vital point
of the overall construction of SI Units. \<close>
lift_definition qequiv ::
"'n['a::dim_type] \<Rightarrow> 'n['b::dim_type] \<Rightarrow> bool" (infix "\<cong>\<^sub>Q" 50) is "(=)" .
subsection\<open>The Equivalence on Abstract SI-\<^theory_text>\<open>Unit\<close>-types\<close>
text\<open>This gives us an equivalence, but, unfortunately, not a congruence.\<close>
subsection\<open>The Equivalence on Abstract SI-\<^theory_text>\<open>Unit\<close>-Types\<close>
text\<open>The latter predicate gives us an equivalence, but, unfortunately, not a congruence.\<close>
lemma qequiv_refl [simp]: "a \<cong>\<^sub>Q a"
by (simp add: qequiv_def)
@ -167,7 +172,7 @@ lemma qeq:
shows "SI('u\<^sub>1) = SI('u\<^sub>2::dim_type)"
by (metis (full_types) qequiv.rep_eq assms fromQ mem_Collect_eq)
subsection\<open>Operations on Abstract Unit types\<close>
subsection\<open>Operations on Abstract SI-Unit-Types\<close>
lift_definition
qtimes :: "('n::comm_ring_1)['a::dim_type] \<Rightarrow> 'n['b::dim_type] \<Rightarrow> 'n['a \<cdot>'b]" (infixl "\<^bold>\<cdot>" 69) is "(*)"

2
src/SI/document/root.tex
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@ -69,7 +69,7 @@ others, like the British Imperial System (BIS).
\parindent 0pt\parskip 0.5ex
\chapter{Introduction to SI Units in Isabelle}
\chapter{SI Units in Isabelle \\ An Introduction}
The International System of Units (SI, abbreviated from the French
Système international (d'unités)) is the modern form of the metric