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(* This file was originally generated by why.
It can be modified; only the generated parts will be overwritten. *)
Require Export search_spec_why.
(* Why obligation from file "/home/jcf/soft/why/examples-c/tutorial/search.c", line 8, characters 16-64: *)
(*Why goal*) Lemma index_impl_po_1 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
(* CADUCEUS_3 *) (0 <= 0 /\
(forall (k:Z), (0 <= k /\ k < 0 -> (acc intM_global (shift t k)) <> v))).
Proof.
intuition.
Save.
(* Why obligation from file "/home/jcf/soft/why/examples-c/tutorial/search.c", line 11, characters 8-12: *)
(*Why goal*) Lemma index_impl_po_2 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
forall (i: Z),
forall (HW_2: (* CADUCEUS_3 *) (0 <= i /\
(forall (k:Z),
(0 <= k /\ k < i -> (acc intM_global (shift t k)) <> v)))),
forall (HW_3: i < n),
forall (result: (pointer global)),
forall (HW_4: result = (shift t i)),
(valid alloc result).
Proof.
intuition; subst; auto.
Save.
(* Why obligation from file "/home/jcf/soft/why/examples-c/tutorial/search.c", line 3, characters 4-105: *)
(*Why goal*) Lemma index_impl_po_3 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
forall (i: Z),
forall (HW_2: (* CADUCEUS_3 *) (0 <= i /\
(forall (k:Z),
(0 <= k /\ k < i -> (acc intM_global (shift t k)) <> v)))),
forall (HW_3: i < n),
forall (result: (pointer global)),
forall (HW_4: result = (shift t i)),
forall (HW_5: (valid alloc result)),
forall (result0: Z),
forall (HW_6: result0 = (acc intM_global result)),
forall (HW_7: result0 = v),
(* CADUCEUS_2 *)
(((0 <= i /\ i < n -> (acc intM_global (shift t i)) = v)) /\
((i = n ->
(forall (i:Z), (0 <= i /\ i < n -> (acc intM_global (shift t i)) <> v))))).
Proof.
intuition.
subst;auto.
Save.
(* Why obligation from file "/home/jcf/soft/why/examples-c/tutorial/search.c", line 8, characters 16-64: *)
(*Why goal*) Lemma index_impl_po_4 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
forall (i: Z),
forall (HW_2: (* CADUCEUS_3 *) (0 <= i /\
(forall (k:Z),
(0 <= k /\ k < i -> (acc intM_global (shift t k)) <> v)))),
forall (HW_3: i < n),
forall (result: (pointer global)),
forall (HW_4: result = (shift t i)),
forall (HW_5: (valid alloc result)),
forall (result0: Z),
forall (HW_6: result0 = (acc intM_global result)),
forall (HW_8: result0 <> v),
forall (i0: Z),
forall (HW_9: i0 = (i + 1)),
(* CADUCEUS_3 *) (0 <= i0 /\
(forall (k:Z), (0 <= k /\ k < i0 -> (acc intM_global (shift t k)) <> v))).
Proof.
intuition.
assert (h : k<i \/ k=i); [ omega | inversion_clear h].
(* case k < i *)
apply (H0 k); auto.
(* case k=i *)
subst; auto.
Save.
(* Why obligation from file "why/search.why", line 19, characters 20-33: *)
(*Why goal*) Lemma index_impl_po_5 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
forall (i: Z),
forall (HW_2: (* CADUCEUS_3 *) (0 <= i /\
(forall (k:Z),
(0 <= k /\ k < i -> (acc intM_global (shift t k)) <> v)))),
forall (HW_3: i < n),
forall (result: (pointer global)),
forall (HW_4: result = (shift t i)),
forall (HW_5: (valid alloc result)),
forall (result0: Z),
forall (HW_6: result0 = (acc intM_global result)),
forall (HW_8: result0 <> v),
forall (i0: Z),
forall (HW_9: i0 = (i + 1)),
(Zwf 0 (n - i0) (n - i)).
Proof.
intuition.
apply H0 with i0; auto with *.
Save.
(* Why obligation from file "/home/jcf/soft/why/examples-c/tutorial/search.c", line 3, characters 4-105: *)
(*Why goal*) Lemma index_impl_po_6 :
forall (t: (pointer global)),
forall (n: Z),
forall (v: Z),
forall (alloc: alloc_table),
forall (intM_global: (memory Z global)),
forall (HW_1: (* CADUCEUS_1 *) (valid_range alloc t 0 (n - 1))),
forall (i: Z),
forall (HW_2: (* CADUCEUS_3 *) (0 <= i /\
(forall (k:Z),
(0 <= k /\ k < i -> (acc intM_global (shift t k)) <> v)))),
forall (HW_10: i >= n),
(* CADUCEUS_2 *)
(((0 <= i /\ i < n -> (acc intM_global (shift t i)) = v)) /\
((i = n ->
(forall (i:Z), (0 <= i /\ i < n -> (acc intM_global (shift t i)) <> v))))).
Proof.
intuition.
(* FILL PROOF HERE *)
Save.
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