Commit dd2efcbf authored by Jean-Christophe Filliâtre's avatar Jean-Christophe Filliâtre
Browse files

a more general pigeon hole principle

parent 4af9081d
...@@ -61,7 +61,7 @@ theory Graph ...@@ -61,7 +61,7 @@ theory Graph
Two cases depending on l3=[] (and thus u=v) conclude the proof. Qed. Two cases depending on l3=[] (and thus u=v) conclude the proof. Qed.
*) *)
clone pigeon.Pigeonhole with type t = vertex clone pigeon.ListAndSet with type t = vertex
predicate cyc_decomp (v: vertex) (l: list vertex) predicate cyc_decomp (v: vertex) (l: list vertex)
(vi: vertex) (l1 l2 l3: list vertex) = (vi: vertex) (l1 l2 l3: list vertex) =
......
...@@ -174,7 +174,7 @@ ...@@ -174,7 +174,7 @@
<proof prover="1"><result status="valid" time="0.04" steps="69"/></proof> <proof prover="1"><result status="valid" time="0.04" steps="69"/></proof>
</goal> </goal>
<goal name="VC relax.0.2" expl="VC for relax" proved="true"> <goal name="VC relax.0.2" expl="VC for relax" proved="true">
<proof prover="11"><result status="valid" time="1.12"/></proof> <proof prover="11"><result status="valid" time="0.54"/></proof>
</goal> </goal>
<goal name="VC relax.0.3" expl="VC for relax" proved="true"> <goal name="VC relax.0.3" expl="VC for relax" proved="true">
<proof prover="1"><result status="valid" time="0.03" steps="117"/></proof> <proof prover="1"><result status="valid" time="0.03" steps="117"/></proof>
...@@ -335,15 +335,15 @@ ...@@ -335,15 +335,15 @@
<proof prover="1"><result status="valid" time="0.02" steps="57"/></proof> <proof prover="1"><result status="valid" time="0.02" steps="57"/></proof>
</goal> </goal>
<goal name="VC bellman_ford.6.1" expl="VC for bellman_ford" proved="true"> <goal name="VC bellman_ford.6.1" expl="VC for bellman_ford" proved="true">
<proof prover="1"><result status="valid" time="1.52" steps="1717"/></proof> <proof prover="1"><result status="valid" time="0.81" steps="1717"/></proof>
</goal> </goal>
</transf> </transf>
</goal> </goal>
<goal name="VC bellman_ford.7" expl="assertion" proved="true"> <goal name="VC bellman_ford.7" expl="assertion" proved="true">
<proof prover="1" timelimit="5"><result status="valid" time="1.07" steps="1190"/></proof> <proof prover="1" timelimit="5"><result status="valid" time="0.55" steps="1190"/></proof>
</goal> </goal>
<goal name="VC bellman_ford.8" expl="loop invariant preservation" proved="true"> <goal name="VC bellman_ford.8" expl="loop invariant preservation" proved="true">
<proof prover="1"><result status="valid" time="0.60" steps="1109"/></proof> <proof prover="1"><result status="valid" time="0.34" steps="1109"/></proof>
</goal> </goal>
<goal name="VC bellman_ford.9" expl="assertion" proved="true"> <goal name="VC bellman_ford.9" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.02" steps="7"/></proof> <proof prover="1"><result status="valid" time="0.02" steps="7"/></proof>
......
(** {1 Pigeon hole principle} (** {1 Pigeon hole principle} *)
module Pigeonhole
use import int.Int
use import map.Map
val lemma pigeonhole (n m: int) (f: int -> int)
requires { 0 <= m < n }
requires { forall i. 0 <= i < n -> 0 <= f i < m }
ensures { exists i1, i2. 0 <= i1 < i2 < n /\ f i1 = f i2 }
end
(* An instance where a list is included into a set with fewer elements.
Contributed by Yuto Takei (University of Tokyo) *) Contributed by Yuto Takei (University of Tokyo) *)
module Pigeonhole module ListAndSet
use import int.Int use import int.Int
use import list.List use import list.List
......
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