equal
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inserted
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335 |
335 |
336 lemma bilinear_rmul: "bilinear h \<Longrightarrow> h x (c *\<^sub>R y) = c *\<^sub>R h x y" |
336 lemma bilinear_rmul: "bilinear h \<Longrightarrow> h x (c *\<^sub>R y) = c *\<^sub>R h x y" |
337 by (simp add: bilinear_def linear_iff) |
337 by (simp add: bilinear_def linear_iff) |
338 |
338 |
339 lemma bilinear_lneg: "bilinear h \<Longrightarrow> h (- x) y = - h x y" |
339 lemma bilinear_lneg: "bilinear h \<Longrightarrow> h (- x) y = - h x y" |
340 by (simp only: scaleR_minus1_left [symmetric] bilinear_lmul) |
340 by (drule bilinear_lmul [of _ "- 1"]) simp |
341 |
341 |
342 lemma bilinear_rneg: "bilinear h \<Longrightarrow> h x (- y) = - h x y" |
342 lemma bilinear_rneg: "bilinear h \<Longrightarrow> h x (- y) = - h x y" |
343 by (simp only: scaleR_minus1_left [symmetric] bilinear_rmul) |
343 by (drule bilinear_rmul [of _ _ "- 1"]) simp |
344 |
344 |
345 lemma (in ab_group_add) eq_add_iff: "x = x + y \<longleftrightarrow> y = 0" |
345 lemma (in ab_group_add) eq_add_iff: "x = x + y \<longleftrightarrow> y = 0" |
346 using add_imp_eq[of x y 0] by auto |
346 using add_imp_eq[of x y 0] by auto |
347 |
347 |
348 lemma bilinear_lzero: |
348 lemma bilinear_lzero: |