diff --git a/test/core.jl b/test/core.jl
index dc74a02275633a..ff2993aee0971b 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -72,15 +72,13 @@ g11840{T<:Tuple}(sig::Type{T}) = 3
 
 g11840b(::DataType) = 1
 g11840b(::Type) = 2
-# FIXME: how to compute that the guard entry is still required,
-# even though Type{Vector} ∩ DataType = Bottom and this method would set cache_with_orig = true
-#g11840b{T<:Tuple}(sig::Type{T}) = 3
+g11840b{T<:Tuple}(sig::Type{T}) = 3
 @test g11840b(Vector) == 2
 @test g11840b(Vector.body) == 1
 @test g11840b(Vector) == 2
 @test g11840b(Vector.body) == 1
-#@test g11840b(Tuple) == 3
-#@test g11840b(TT11840) == 3
+@test g11840b(Tuple) == 3
+@test g11840b(TT11840) == 3
 
 h11840(::DataType) = '1'
 h11840(::Type) = '2'
diff --git a/test/inference.jl b/test/inference.jl
index 67c31880cbe024..cb685f5ddad953 100644
--- a/test/inference.jl
+++ b/test/inference.jl
@@ -494,3 +494,28 @@ immutable MyType18457{T,F,G}<:AbstractMyType18457{T,F,G} end
 tpara18457{I}(::Type{AbstractMyType18457{I}}) = I
 tpara18457{A<:AbstractMyType18457}(::Type{A}) = tpara18457(supertype(A))
 @test tpara18457(MyType18457{true}) === true
+
+# Issue #12580
+abstract AbstractMyType12580{T}
+immutable MyType12580{T}<:AbstractMyType12580{T} end
+tpara{A<:AbstractMyType12580}(::Type{A}) = tpara(supertype(A))
+tpara{I}(::Type{AbstractMyType12580{I}}) = I
+@test tpara(MyType12580{true})
+
+# Issue #18348
+f18348{T<:Any}(::Type{T}, x) = 1
+f18348{T<:Any}(::Type{T}, x::T) = 2
+@test length(methods(f18348, Tuple{Type{Any},Any})) == 1
+
+# Issue #13165
+@test Symmetric{Float64,Matrix{Float64}} <: LinAlg.RealHermSymComplexHerm
+@test Hermitian{Float64,Matrix{Float64}} <: LinAlg.RealHermSymComplexHerm
+@test Hermitian{Complex{Float64},Matrix{Complex{Float64}}} <: LinAlg.RealHermSymComplexHerm
+
+# Issue #11803
+@test TypeVar(:T, Int) <: Int
+@test TypeVar(:T, Union{Int,Float64}) <: Union{Int,Float64}
+
+# Issue #12721
+f12721{T<:Type{Int}}(::T) = true;
+@test_throws MethodError f12721(Float64)