Inductive Sfor_inv {cs: compspecs} (Delta: tycontext):
  forall (_i: ident) (m: Z) (hi: expr) (n: Z)
         (assert_callee: Z -> environ -> mpred)
         (inv0: environ -> mpred)
         (inv1 inv2: Z -> environ -> mpred), Prop :=
| construct_Sfor_inv: forall _i m hi n assert_callee inv0 inv1,
    (forall i i', exists inv0' inv0'' inv1' inv1'', Sfor_inv_rec Delta _i i' m hi n (assert_callee i) inv0'' inv1'' /\ inv0' i' = inv0'' /\ inv0 i = inv0' /\ inv1' i' = inv1'' /\ inv1 i = inv1') ->
    Sfor_inv Delta _i m hi n assert_callee (EX i: Z, inv0 i i) (fun i => inv1 i i) (fun i => inv1 (i+1) i).Inductive Sfor_inv {cs: compspecs} (Delta: tycontext):
  forall (_i: ident) (m: Z) (hi: expr) (n: Z)
         (assert_callee: Z -> environ -> mpred)
         (inv0: environ -> mpred)
         (inv1 inv2: Z -> environ -> mpred), Prop :=
| construct_Sfor_inv: forall _i m hi n assert_callee inv0 inv1,
    (forall i i', exists inv0' inv0'' inv1' inv1'', Sfor_inv_rec Delta _i i' m hi n (assert_callee i) inv0'' inv1'' /\ inv0' i' = inv0'' /\ inv0 i = inv0' /\ inv1' i' = inv1'' /\ inv1 i = inv1') ->
    Sfor_inv Delta _i m hi n assert_callee (EX i: Z, inv0 i i) (fun i => inv1 i i) (fun i => inv1 (i+1) i).

(* Specifications: *)
Lemma typed_false_tint_e: forall v, typed_false tint v -> v = Vint Int.zero.
Lemma CLASSIFY_CMP: classify_cmp type_i (typeof hi) = cmp_default.
Lemma Sfor_comparison_Signed_I32: forall i n', Int6432_val (typeof hi) n' n -> classify_binarith type_i (typeof hi) = bin_case_i Signed -> m <= i <= n -> force_val (sem_cmp_default Clt type_i (typeof hi) (Vint (Int.repr i)) n') = Vint Int.zero <-> i >= n.
Lemma Sfor_comparison_Unsigned_I32: forall i n', Int6432_val (typeof hi) n' n -> classify_binarith type_i (typeof hi) = bin_case_i Unsigned -> m <= i <= n -> force_val (sem_cmp_default Clt type_i (typeof hi) (Vint (Int.repr i)) n') = Vint Int.zero <-> i >= n.
Lemma Sfor_comparison_Signed_I64: forall i n', Int6432_val (typeof hi) n' n -> classify_binarith type_i (typeof hi) = bin_case_l Signed -> m <= i <= n -> force_val (sem_cmp_default Clt type_i (typeof hi) (Vint (Int.repr i)) n') = Vint Int.zero <-> i >= n.
Lemma Sfor_comparison_Unsigned_I64: forall i n', Int6432_val (typeof hi) n' n -> classify_binarith type_i (typeof hi) = bin_case_l Unsigned -> m <= i <= n -> force_val (sem_cmp_default Clt type_i (typeof hi) (Vint (Int.repr i)) n') = Vint Int.zero <-> i >= n.