src/HOL/Old_Number_Theory/IntPrimes.thy
changeset 49962 a8cc904a6820
parent 47163 248376f8881d
child 57512 cc97b347b301
equal deleted inserted replaced
49961:d3d2b78b1c19 49962:a8cc904a6820
   339 text {* \medskip @{term xzgcd} linear *}
   339 text {* \medskip @{term xzgcd} linear *}
   340 
   340 
   341 lemma xzgcda_linear_aux1:
   341 lemma xzgcda_linear_aux1:
   342   "(a - r * b) * m + (c - r * d) * (n::int) =
   342   "(a - r * b) * m + (c - r * d) * (n::int) =
   343    (a * m + c * n) - r * (b * m + d * n)"
   343    (a * m + c * n) - r * (b * m + d * n)"
   344   by (simp add: left_diff_distrib right_distrib mult_assoc)
   344   by (simp add: left_diff_distrib distrib_left mult_assoc)
   345 
   345 
   346 lemma xzgcda_linear_aux2:
   346 lemma xzgcda_linear_aux2:
   347   "r' = s' * m + t' * n ==> r = s * m + t * n
   347   "r' = s' * m + t' * n ==> r = s * m + t * n
   348     ==> (r' mod r) = (s' - (r' div r) * s) * m + (t' - (r' div r) * t) * (n::int)"
   348     ==> (r' mod r) = (s' - (r' div r) * s) * m + (t' - (r' div r) * t) * (n::int)"
   349   apply (rule trans)
   349   apply (rule trans)