compute with an invariant in validated integ

validated_integ_invariant

$ git diff
diff --git a/REQUIRE b/REQUIRE
index ba1d010..87bc2e0 100644
--- a/REQUIRE
+++ b/REQUIRE
@@ -4,3 +4,4 @@ TaylorSeries v0.8.1
 IntervalArithmetic v0.15.1
 TaylorIntegration v0.4.0
 RecipesBase
+LazySets
diff --git a/src/validatedODEs.jl b/src/validatedODEs.jl
index 6e1f278..2743bcb 100644
--- a/src/validatedODEs.jl
+++ b/src/validatedODEs.jl
@@ -1,4 +1,6 @@

 # Some methods for validated integration of ODEs
+using LazySets
+using TaylorModels: Interval

 """
     remainder_taylorstep!(f!, t, x, dx, xI, dxI, δI, δt)
@@ -163,7 +165,7 @@ function validated_step!(f!, t::Taylor1{T},
         rem::Vector{Interval{T}}, δq_norm::IntervalBox{N,T},
         q0::IntervalBox{N,T}, q0box::IntervalBox{N,T}, nsteps::Int,
         orderT::Int, abstol::T, parse_eqs::Bool,
-        check_property::Function=(t, x)->true) where {N,T}
+        check_property::Function=(t, x)->true, invariant::LazySet=Universe(length(δq_norm))) where {N,T}
     #
     # One step integration (non-validated)
     δt = TaylorIntegration.taylorstep!(f!, t, x, dx, xaux,
@@ -199,6 +201,10 @@ function validated_step!(f!, t::Taylor1{T},
             end
             xv[nsteps] = evaluate(xTMN, δq_norm) # IntervalBox

+            if is_intersection_empty(convert(Hyperrectangle, xv[nsteps]), invariant)
+                break
+            end
+
             if !check_property(t0+δt, xv[nsteps])
                 δt = δt/2
                 continue
@@ -220,11 +226,10 @@ function validated_step!(f!, t::Taylor1{T},
     return δt
 end

-
 function validated_integ(f!, qq0::AbstractArray{T,1}, δq0::IntervalBox{N,T},
         t0::T, tmax::T, orderQ::Int, orderT::Int, abstol::T;
         maxsteps::Int=500, parse_eqs::Bool=true,
-        check_property::Function=(t, x)->true) where {N, T<:Real}
+        check_property::Function=(t, x)->true, invariant::LazySet=Universe(length(qq0))) where {N, T<:Real}

     # Set proper parameters for jet transport
     @assert N == get_numvars()
@@ -297,7 +302,7 @@ function validated_integ(f!, qq0::AbstractArray{T,1}, δq0::IntervalBox{N,T},
         # Validated step of the integration
         δt = validated_step!(f!, t, x, dx, xaux, tI, xI, dxI, xauxI,
             t0, tmax, x0, x0I, xTMN, xv, rem, δq_norm,
-            q0, q0box, nsteps, orderT, abstol, parse_eqs, check_property)
+            q0, q0box, nsteps, orderT, abstol, parse_eqs, check_property, invariant)

         # New initial conditions and time
         nsteps += 1