val lemma_shift_define_all (_:unit) : Lemma
  (forall (p:poly) (n:int) (i:int).{:pattern (shift p n).[i]} (shift p n).[i] == (p.[i - n] && i >= 0))
let lemma_shift_define_all () =
  FStar.Classical.forall_intro_2_with_pat (fun p n -> shift p n) lemma_shift_define
val lemma_shift_define_all (_:unit) : Lemma
  (forall (p:poly) (n:int) (i:int).{:pattern (shift p n).[i]} (shift p n).[i] == (p.[i - n] && i >= 0))
let lemma_shift_define_all () =
FStar.Classical.forall_intro_2_with_pat (fun p n -> shift p n) lemma_shift_define
Vale.Math.Poly2.Lemmas.fst.checked
prims.fst.checked FStar.Pervasives.fsti.checked FStar.Mul.fst.checked FStar.Math.Lib.fst.checked FStar.List.fst.checked FStar.Classical.fsti.checked FStar.Calc.fsti.checked
Vale.Math.Poly2.Lemmas.fst
Prims.unit FStar.Classical.forall_intro_2_with_pat Vale.Math.Poly2_s.poly Prims.int Prims.l_Forall Prims.eq2 Prims.bool Vale.Math.Poly2_s.op_String_Access Vale.Math.Poly2_s.shift Prims.op_AmpAmp Prims.op_Subtraction Prims.op_GreaterThanOrEqual Vale.Math.Poly2.Lemmas.lemma_shift_define
module Vale.Math.Poly2.Lemmas
open FStar.Mul

let lemma_pointwise_equal a b pf =
  FStar.Classical.forall_intro pf;
  lemma_equal a b

let lemma_index a =
  FStar.Classical.forall_intro (lemma_index_i a)

let lemma_index_all () =
  FStar.Classical.forall_intro_2 lemma_index_i

let lemma_zero_define () =
  FStar.Classical.forall_intro lemma_zero_define_i

let lemma_one_define () =
  FStar.Classical.forall_intro lemma_one_define_i

let lemma_monomial_define n =
  FStar.Classical.forall_intro (lemma_monomial_define_i n)

let lemma_monomial_define_all () =
  FStar.Classical.forall_intro_with_pat (fun n -> monomial n) lemma_monomial_define

let lemma_ones_define n =
  FStar.Classical.forall_intro (lemma_ones_define_i n)

let lemma_ones_define_all () =
  FStar.Classical.forall_intro_with_pat (fun n -> ones n) lemma_ones_define

let lemma_shift_define p n =
  FStar.Classical.forall_intro (lemma_shift_define_i p n)

let lemma_shift_define_forward p n =
  lemma_shift_define p n
val lemma_shift_define_all (_:unit) : Lemma
  (forall (p:poly) (n:int) (i:int).{:pattern (shift p n).[i]} (shift p n).[i] == (p.[i - n] && i >= 0))
_: Prims.unit
  -> FStar.Pervasives.Lemma
    (ensures
      forall (p: Vale.Math.Poly2_s.poly) (n: Prims.int) (i: Prims.int).
        {:pattern (Vale.Math.Poly2_s.shift p n).[ i ]}
        (Vale.Math.Poly2_s.shift p n).[ i ] == (p.[ i - n ] && i >= 0))