src/HOL/NumberTheory/Fib.thy
changeset 23431 25ca91279a9b
parent 23365 f31794033ae1
child 23688 7cd68def72b2
equal deleted inserted replaced
23430:771117253634 23431:25ca91279a9b
    83 theorem fib_Cassini:
    83 theorem fib_Cassini:
    84  "fib (Suc (Suc n)) * fib n =
    84  "fib (Suc (Suc n)) * fib n =
    85   (if n mod 2 = 0 then fib (Suc n) * fib (Suc n) - 1
    85   (if n mod 2 = 0 then fib (Suc n) * fib (Suc n) - 1
    86    else fib (Suc n) * fib (Suc n) + 1)"
    86    else fib (Suc n) * fib (Suc n) + 1)"
    87   apply (rule int_int_eq [THEN iffD1]) 
    87   apply (rule int_int_eq [THEN iffD1]) 
    88   apply (simp add: fib_Cassini_int del: of_nat_mult) 
    88   apply (simp add: fib_Cassini_int)
    89   apply (subst zdiff_int [symmetric]) 
    89   apply (subst zdiff_int [symmetric]) 
    90    apply (insert fib_Suc_gr_0 [of n], simp_all)
    90    apply (insert fib_Suc_gr_0 [of n], simp_all)
    91   done
    91   done
    92 
    92 
    93 
    93