val lemma_shift_define_forward (p:poly) (n:int) : Lemma
  (forall (i:int).{:pattern p.[i]} (shift p n).[i + n] == (p.[i] && i + n >= 0))
let lemma_shift_define_forward p n =
  lemma_shift_define p n
val lemma_shift_define_forward (p:poly) (n:int) : Lemma
  (forall (i:int).{:pattern p.[i]} (shift p n).[i + n] == (p.[i] && i + n >= 0))
let lemma_shift_define_forward p n =
lemma_shift_define p n
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
Vale.Math.Poly2_s.poly Prims.int Vale.Math.Poly2.Lemmas.lemma_shift_define Prims.unit
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)
val lemma_shift_define_forward (p:poly) (n:int) : Lemma
  (forall (i:int).{:pattern p.[i]} (shift p n).[i + n] == (p.[i] && i + n >= 0))
p: Vale.Math.Poly2_s.poly -> n: Prims.int
  -> FStar.Pervasives.Lemma
    (ensures
      forall (i: Prims.int). {:pattern p.[ i ]}
        (Vale.Math.Poly2_s.shift p n).[ i + n ] == (p.[ i ] && i + n >= 0))