isahipster: e9cba2ffd3225e111ce71b29426a588bf0f80c26

     1: theory prop_23
     2: imports Main
     3:         "$HIPSTER_HOME/IsaHipster"
     4: begin
     5:   datatype 'a list = Nil2 | Cons2 "'a" "'a list"
     6:   datatype Nat = Z | S "Nat"
     7:   fun length :: "'a list => Nat" where
     8:   "length (Nil2) = Z"
     9:   | "length (Cons2 y xs) = S (length xs)"
    10:   fun half :: "Nat => Nat" where
    11:   "half (Z) = Z"
    12:   | "half (S (Z)) = Z"
    13:   | "half (S (S z)) = S (half z)"
    14:   fun append :: "'a list => 'a list => 'a list" where
    15:   "append (Nil2) y = y"
    16:   | "append (Cons2 z xs) y = Cons2 z (append xs y)"
    17:   (*hipster length half append *)
    18: 
    19: lemma lemma_a [thy_expl]: "append x2 Nil2 = x2"
    20: by (hipster_induct_schemes length.simps append.simps)
    21: 
    22: lemma lemma_aa [thy_expl]: "append (append x1 y1) z1 = append x1 (append y1 z1)"
    23: by (hipster_induct_schemes length.simps append.simps)
    24: 
    25: lemma unknown []: "length (append x y) = length (append y x)"
    26: oops
    27: 
    28: (*hipster length half append*)
    29: 
    30: lemma ax2[thy_expl]: "length (append y (Cons2 ya xs)) = S (length (append y xs))"
    31: by(hipster_induct_schemes)
    32: 
    33:   theorem x0 :
    34:     "(half (length (append x y))) = (half (length (append y x)))"
    35:     by (hipster_induct_schemes length.simps append.simps half.simps list.exhaust Nat.exhaust)
    36:     by (tactic {* Subgoal.FOCUS_PARAMS (K (Tactic_Data.hard_tac @{context})) @{context} 1 *})
    37: end