equal
deleted
inserted
replaced
129 lemma hypreal_sqrt_hrabs2 [simp]: "!!x. ( *f* sqrt)(x*x) = abs(x)" |
129 lemma hypreal_sqrt_hrabs2 [simp]: "!!x. ( *f* sqrt)(x*x) = abs(x)" |
130 by (transfer, simp) |
130 by (transfer, simp) |
131 |
131 |
132 lemma hypreal_sqrt_hyperpow_hrabs [simp]: |
132 lemma hypreal_sqrt_hyperpow_hrabs [simp]: |
133 "!!x. ( *f* sqrt)(x pow (hypnat_of_nat 2)) = abs(x)" |
133 "!!x. ( *f* sqrt)(x pow (hypnat_of_nat 2)) = abs(x)" |
134 by (unfold hyperpow_def, transfer, simp) |
134 by (transfer, simp) |
135 |
135 |
136 lemma star_sqrt_HFinite: "\<lbrakk>x \<in> HFinite; 0 \<le> x\<rbrakk> \<Longrightarrow> ( *f* sqrt) x \<in> HFinite" |
136 lemma star_sqrt_HFinite: "\<lbrakk>x \<in> HFinite; 0 \<le> x\<rbrakk> \<Longrightarrow> ( *f* sqrt) x \<in> HFinite" |
137 apply (rule HFinite_square_iff [THEN iffD1]) |
137 apply (rule HFinite_square_iff [THEN iffD1]) |
138 apply (simp only: hypreal_sqrt_mult_distrib2 [symmetric], simp) |
138 apply (simp only: hypreal_sqrt_mult_distrib2 [symmetric], simp) |
139 done |
139 done |