MLKEM_avx2_encdec.ec: make some proofs faster

proof/correctness/avx2/MLKEM_avx2_encdec.ec

@@ -358,17 +358,53 @@ have Hjm: (0 <= j < 0 + 8). rewrite Hj => />. move :Hjm. rewrite -mema_iota -iot
 rewrite !modzDml -addrA !modzDml -!addrA !modzDml -!addrA !modzDml !modz_dvd //=.
 do 8!(try (move => Hjm; case Hjm => />); first by smt()). qed.
 
+lemma fill0 f k (t : ipoly): fill f k 0 t = t.
+proof.
+rewrite /fill &(Array256.tP) /= => i *.
+by rewrite !initE /#.
+qed.
+
+lemma fillSm f k n (t : ipoly): 0 < n =>
+  fill f k n t = fill f (k+1) (n-1) t.[k <- f k].
+proof.
+move=> ge0_n @/fill; apply/Array256.tP => i rg_i.
+by rewrite !initE /= get_set_if /#.
+qed.
+
+lemma fill_swap (i j ki kj : int) f g (t : ipoly) :
+  i + ki <= j => fill f i ki (fill g j kj t) = fill g j kj (fill f i ki t).
+proof.
+move=> rg @/fill; apply/Array256.tP => k *.
+do rewrite initE /=. smt().
+qed.
+
+op [opaque] fillC ['a] = Array256.fill<:'a>.
+
+lemma fillCE ['a] : fillC<:'a> = Array256.fill.
+proof. by rewrite /fillC. qed.
+
+lemma fillC_swap (i j ki kj : int) f g (t : ipoly) :
+  i + ki <= j => fillC f i ki (fillC g j kj t) = fillC g j kj (fillC f i ki t).
+proof. by rewrite !fillCE &(fill_swap). qed.
+
+lemma fillC0 f k (t : ipoly): fillC f k 0 t = t.
+proof. by rewrite fillCE &(fill0). qed.
+
+lemma fillCSm f k n (t : ipoly): 0 < n =>
+  fillC f k n t = fillC f (k+1) (n - 1) t.[k <- f k].
+proof. by rewrite fillCE &(fillSm). qed.
+
+hint simplify fillC_swap.
+
 equiv eq_decode1_opt :
   EncDec_AVX2.decode1_opt ~ EncDec.decode1 : 
     ={a} ==> ={res}.
 proc.
 unroll for {1} ^while.
 do 8!(unroll for {1} ^while).
 unroll for {2} ^while.
-auto => /> &m.
-apply tP_red256.
-move => i. 
-(* FIXME: TOO LONG  => *) do 255!(move => Hi; case Hi => |>). 
+auto=> /= &1 &2 ->; rewrite -!fillCE /=.
+by do 32! ((do 8! rewrite fillCSm 1://); rewrite /= fillC0).
 qed.
 
 equiv decode10_vec_corr:
@@ -392,23 +428,23 @@ proof.
     unroll for {2} 2.
     wp; skip; auto => />.
     move => &1 &2 [#] k_lb k_ub c_eq k_tub />.
-    rewrite (mulzDr 320 _ _) (mulzDr 256 _ _) mulz1 //=.
+    rewrite (mulzDr 320 _ _) (mulzDr 256 _ _) mulz1 /=.
     split.
       + move : k_lb k_tub => /#.
       + move => j j_lb j_ub.
-        rewrite filliE 1:/# //=.
-        rewrite j_ub //=.
+        rewrite filliE 1:/# ~-1://=.
+        rewrite j_ub ~-1://=.
         case (j < 256 * k{2}) => j_tub.
           + have -> /=: !(256 * k{2} <= j). by rewrite -ltzNge j_tub.
             rewrite c_eq; first by rewrite j_lb j_tub.
-            do (rewrite Array768.set_neqiE 1:/#; first by move : j_tub j_lb => /#).
-            done.
+            rewrite !Array768.get_set_if ~-1://.
+            by have /#: k{2} = 1 \/ k{2} = 2 by smt().
           + move : j_tub => /lezNgt j_tlb.
             rewrite j_tlb /=.
             have j_iota: j \in iota_ (256*k{2}) 256; first by rewrite mem_iota j_ub j_tlb.
-            move : j_iota.
-            do (rewrite Array768.get_setE 1:/#).
-            smt(mem_iota).
+            move : j_iota; rewrite !Array768.get_set_if ~-1://.
+            have: k{2} = 0 \/ k{2} = 1 \/ k{2} = 2 by smt().
+            by rewrite -iotaredE /=; do 2! (move=> [#|] -> /=).
   auto => />.
   move => cL cR k k_tlb _ k_lb k_ub.
   have -> /=: k = 3. move : k_tlb k_ub => /#.