Commit 3165a4c5 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Use new set notation for multisets in tests.

parent 5d8dd980
......@@ -27,48 +27,45 @@ Section test.
2 < multiplicity x X X Y 1 < multiplicity x Y.
Proof. multiset_solver. Qed.
Lemma test_multiplicity_2 x X :
2 < multiplicity x X {[ x ]} {[ x ]} {[ x ]} X.
2 < multiplicity x X {[ x ;+ x ;+ x ]} X.
Proof. multiset_solver. Qed.
Lemma test_multiplicity_3 x X :
multiplicity x X < 3 {[ x ]} {[ x ]} {[ x ]} X.
multiplicity x X < 3 {[ x ;+ x ;+ x ]} X.
Proof. multiset_solver. Qed.
Lemma test_elem_of_1 x X : x X {[x]} X.
Proof. multiset_solver. Qed.
Lemma test_elem_of_2 x X : x X {[x]} X.
Proof. multiset_solver. Qed.
Lemma test_elem_of_3 x y X : x y x X y X {[x]} {[y]} X.
Lemma test_elem_of_3 x y X : x y x X y X {[x ;+ y]} X.
Proof. multiset_solver. Qed.
Lemma test_elem_of_4 x y X Y : x y x X y Y {[x]} {[y]} X Y.
Lemma test_elem_of_4 x y X Y : x y x X y Y {[x ;+ y]} X Y.
Proof. multiset_solver. Qed.
Lemma test_elem_of_5 x y X Y : x y x X y Y {[x]} (X Y) {[ y ]}.
Proof. multiset_solver. Qed.
Lemma test_elem_of_6 x y X : {[x]} {[y]} X x X y X.
Lemma test_elem_of_6 x y X : {[x ;+ y]} X x X y X.
Proof. multiset_solver. Qed.
Lemma test_big_1 x1 x2 x3 x4 :
{[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]} @{gmultiset A}
{[ x1 ]} {[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]}.
{[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]} @{gmultiset A}
{[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]}.
Proof. multiset_solver. Qed.
Lemma test_big_2 x1 x2 x3 x4 X :
2 multiplicity x4 X
{[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]} @{gmultiset A}
{[ x1 ]} {[ x1 ]} {[ x2 ]} {[ x3 ]} X.
{[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]} @{gmultiset A}
{[ x1 ;+ x1 ;+ x2 ;+ x3 ]} X.
Proof. multiset_solver. Qed.
Lemma test_big_3 x1 x2 x3 x4 X :
4 multiplicity x4 X
{[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]}
{[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]}
{[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]}
@{gmultiset A}
{[ x1 ]} {[ x1 ]} {[ x2 ]} {[ x3 ]}
{[ x1 ]} {[ x1 ]} {[ x2 ]} {[ x3 ]} X.
{[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x1 ;+ x1 ;+ x2 ;+ x3 ]} X.
Proof. multiset_solver. Qed.
Lemma test_big_4 x1 x2 x3 x4 x5 x6 x7 x8 x9 :
{[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]}
{[ x5 ]} {[ x6 ]} {[ x7 ]} {[ x8 ]} {[ x8 ]} {[ x9 ]}
{[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+ x5 ;+ x6 ;+ x7 ;+ x8 ;+ x8 ;+ x9 ]}
@{gmultiset A}
{[ x1 ]} {[ x1 ]} {[ x2 ]} {[ x3 ]} {[ x4 ]} {[ x4 ]}
{[ x5 ]} {[ x5 ]} {[ x6 ]} {[ x7 ]} {[ x9 ]} {[ x8 ]} {[ x8 ]}.
{[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+
x5 ;+ x5 ;+ x6 ;+ x7 ;+ x9 ;+ x8 ;+ x8 ]}.
Proof. multiset_solver. Qed.
Lemma test_firstorder_1 (P : A Prop) x X :
......
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