equal
deleted
inserted
replaced
43 |
43 |
44 instantiation star :: (scaleR) scaleR |
44 instantiation star :: (scaleR) scaleR |
45 begin |
45 begin |
46 |
46 |
47 definition |
47 definition |
48 star_scaleR_def [transfer_unfold, code del]: "scaleR r \<equiv> *f* (scaleR r)" |
48 star_scaleR_def [transfer_unfold]: "scaleR r \<equiv> *f* (scaleR r)" |
49 |
49 |
50 instance .. |
50 instance .. |
51 |
51 |
52 end |
52 end |
53 |
53 |
109 |
109 |
110 subsection {* Injection from @{typ hypreal} *} |
110 subsection {* Injection from @{typ hypreal} *} |
111 |
111 |
112 definition |
112 definition |
113 of_hypreal :: "hypreal \<Rightarrow> 'a::real_algebra_1 star" where |
113 of_hypreal :: "hypreal \<Rightarrow> 'a::real_algebra_1 star" where |
114 [transfer_unfold, code del]: "of_hypreal = *f* of_real" |
114 [transfer_unfold]: "of_hypreal = *f* of_real" |
115 |
115 |
116 lemma Standard_of_hypreal [simp]: |
116 lemma Standard_of_hypreal [simp]: |
117 "r \<in> Standard \<Longrightarrow> of_hypreal r \<in> Standard" |
117 "r \<in> Standard \<Longrightarrow> of_hypreal r \<in> Standard" |
118 by (simp add: of_hypreal_def) |
118 by (simp add: of_hypreal_def) |
119 |
119 |
433 *) |
433 *) |
434 |
434 |
435 subsection{*Powers with Hypernatural Exponents*} |
435 subsection{*Powers with Hypernatural Exponents*} |
436 |
436 |
437 definition pow :: "['a::power star, nat star] \<Rightarrow> 'a star" (infixr "pow" 80) where |
437 definition pow :: "['a::power star, nat star] \<Rightarrow> 'a star" (infixr "pow" 80) where |
438 hyperpow_def [transfer_unfold, code del]: "R pow N = ( *f2* op ^) R N" |
438 hyperpow_def [transfer_unfold]: "R pow N = ( *f2* op ^) R N" |
439 (* hypernatural powers of hyperreals *) |
439 (* hypernatural powers of hyperreals *) |
440 |
440 |
441 lemma Standard_hyperpow [simp]: |
441 lemma Standard_hyperpow [simp]: |
442 "\<lbrakk>r \<in> Standard; n \<in> Standard\<rbrakk> \<Longrightarrow> r pow n \<in> Standard" |
442 "\<lbrakk>r \<in> Standard; n \<in> Standard\<rbrakk> \<Longrightarrow> r pow n \<in> Standard" |
443 unfolding hyperpow_def by simp |
443 unfolding hyperpow_def by simp |