src/HOL/Library/FrechetDeriv.thy
changeset 34146 14595e0c27e8
parent 32960 69916a850301
child 36361 1debc8e29f6a
equal deleted inserted replaced
34145:402b7c74799d 34146:14595e0c27e8
   436     assume "norm (h - 0) < norm x"
   436     assume "norm (h - 0) < norm x"
   437     hence "h \<noteq> -x" by clarsimp
   437     hence "h \<noteq> -x" by clarsimp
   438     hence 2: "x + h \<noteq> 0"
   438     hence 2: "x + h \<noteq> 0"
   439       apply (rule contrapos_nn)
   439       apply (rule contrapos_nn)
   440       apply (rule sym)
   440       apply (rule sym)
   441       apply (erule equals_zero_I)
   441       apply (erule minus_unique)
   442       done
   442       done
   443     show "norm (?inv (x + h) - ?inv x - - (?inv x * h * ?inv x)) / norm h
   443     show "norm (?inv (x + h) - ?inv x - - (?inv x * h * ?inv x)) / norm h
   444           = norm ((?inv (x + h) - ?inv x) * h * ?inv x) / norm h"
   444           = norm ((?inv (x + h) - ?inv x) * h * ?inv x) / norm h"
   445       apply (subst inverse_diff_inverse [OF 2 x])
   445       apply (subst inverse_diff_inverse [OF 2 x])
   446       apply (subst minus_diff_minus)
   446       apply (subst minus_diff_minus)