mmtheorems96 - Metamath Proof Explorer

Home	Metamath Proof Explorer	< Previous Next >
		Browser slow? Try the Unicode version.

Jump to page: Contents + 1 1-100 2 101-200 3 201-300 4 301-400 5 401-500 6 501-600 7 601-700 8 701-800 9 801-900 10 901-1000 11 1001-1100 12 1101-1200 13 1201-1300 14 1301-1400 15 1401-1500 16 1501-1600 17 1601-1700 18 1701-1800 19 1801-1900 20 1901-2000 21 2001-2100 22 2101-2200 23 2201-2300 24 2301-2400 25 2401-2500 26 2501-2600 27 2601-2700 28 2701-2800 29 2801-2900 30 2901-3000 31 3001-3100 32 3101-3200 33 3201-3300 34 3301-3400 35 3401-3500 36 3501-3600 37 3601-3700 38 3701-3800 39 3801-3900 40 3901-4000 41 4001-4100 42 4101-4200 43 4201-4300 44 4301-4400 45 4401-4500 46 4501-4600 47 4601-4700 48 4701-4800 49 4801-4900 50 4901-5000 51 5001-5100 52 5101-5200 53 5201-5300 54 5301-5400 55 5401-5500 56 5501-5600 57 5601-5700 58 5701-5800 59 5801-5900 60 5901-6000 61 6001-6100 62 6101-6200 63 6201-6300 64 6301-6400 65 6401-6500 66 6501-6600 67 6601-6700 68 6701-6800 69 6801-6900 70 6901-7000 71 7001-7100 72 7101-7200 73 7201-7300 74 7301-7400 75 7401-7500 76 7501-7600 77 7601-7700 78 7701-7800 79 7801-7900 80 7901-8000 81 8001-8100 82 8101-8200 83 8201-8300 84 8301-8400 85 8401-8500 86 8501-8600 87 8601-8700 88 8701-8800 89 8801-8900 90 8901-9000 91 9001-9100 92 9101-9200 93 9201-9300 94 9301-9400 95 9401-9500 96 9501-9600 97 9601-9700 98 9701-9800 99 9801-9900 100 9901-10000 101 10001-10100 102 10101-10200 103 10201-10300 104 10301-10400 105 10401-10500 106 10501-10600 107 10601-10687

Color key:

Metamath Proof Explorer (1-8759)

Hilbert Space Explorer (8760-10687)

**Statement List for Metamath Proof Explorer -** 9501-9600 - Page 96 of 107
Type	Label	Description
Statement

Theorem	pjoml2 9501	Variation of orthomodular law. Definition in [Kalmbach] p. 22.


Theorem	pjoml3 9502	Variation of orthomodular law.


Theorem	pjoml4 9503	Variation of orthomodular law.


Theorem	pjoml5 9504	The orthomodular law. Remark in [Kalmbach] p. 22.


Theorem	pjoml6 9505	An equivalent of the orthomodular law. Theorem 29.13(e) of [MaedaMaeda] p. 132.
$/\$

Theorem	cmbr 9506	Binary relation expressing the commutes relation. Definition of commutes in [Kalmbach] p. 20.


Theorem	cmcmlem 9507	Commutation is symmetric. Theorem 3.4 of [Beran] p. 45.


Theorem	cmcm 9508	Commutation is symmetric. Theorem 2(v) of [Kalmbach] p. 22.


Theorem	cmcm2 9509	Commutation with orthocomplement. Theorem 2.3(i) of [Beran] p. 39.


Theorem	cmcm3 9510	Commutation with orthocomplement. Remark in [Kalmbach] p. 23.


Theorem	cmcm4 9511	Commutation with orthocomplement. Remark in [Kalmbach] p. 23.


Theorem	cmbr2 9512	Alternate definition of the commutes relation. Remark in [Kalmbach] p. 23.


Theorem	cmcmi 9513	Commutation is symmetric. Theorem 2(v) of [Kalmbach] p. 22.


Theorem	cmcm2i 9514	Commutation with orthocomplement. Theorem 2.3(i) of [Beran] p. 39.


Theorem	cmcm3i 9515	Commutation with orthocomplement. Remark in [Kalmbach] p. 23.


Theorem	cmbr3 9516	Alternate definition for the commutes relation. Lemma 3 of [Kalmbach] p. 23.


Theorem	cmbr4 9517	Alternate definition for the commutes relation.


Theorem	lecm 9518	Comparable Hilbert lattice elements commute. Theorem 2.3(iii) of [Beran] p. 40.


Theorem	lecmi 9519	Comparable Hilbert lattice elements commute. Theorem 2.3(iii) of [Beran] p. 40.


Theorem	cmj1 9520	A Hilbert lattice element commutes with its join.


Theorem	cmj2 9521	A Hilbert lattice element commutes with its join.


Theorem	cmm1 9522	A Hilbert lattice element commutes with its meet.


Theorem	cmm2 9523	A Hilbert lattice element commutes with its meet.


Theorem	cmbr3t 9524	Alternate definition for the commutes relation. Lemma 3 of [Kalmbach] p. 23.
$/\$

Theorem	cm0t 9525	The zero Hilbert lattice element commutes with every element.


Theorem	cmid 9526	The commutes relation is reflexive.


Theorem	pjoml2t 9527	Variation of orthomodular law. Definition in [Kalmbach] p. 22.
$/\$ $/\$

Theorem	pjoml3t 9528	Variation of orthomodular law.
$/\$

Theorem	pjoml5t 9529	The orthomodular law. Remark in [Kalmbach] p. 22.
$/\$

Theorem	cmcmt 9530	Commutation is symmetric. Theorem 2(v) of [Kalmbach] p. 22.
$/\$

Theorem	cmcm3t 9531	Commutation with orthocomplement. Remark in [Kalmbach] p. 23.
$/\$

Theorem	cmcm2t 9532	Commutation with orthocomplement. Theorem 2.3(i) of [Beran] p. 39.
$/\$

Theorem	lecmt 9533	Comparable Hilbert lattice elements commute. Theorem 2.3(iii) of [Beran] p. 40.
$/\$ $/\$

Foulis-Holland theorem

Theorem	fh1t 9534	Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular lattice elements commute, the triple is distributive. First of two parts. Theorem 5 of [Kalmbach] p. 25.
$/\$ $/\$ $/\$ $/\$

Theorem	fh2t 9535	Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular lattice elements commute, the triple is distributive. Second of two parts. Theorem 5 of [Kalmbach] p. 25.
$/\$ $/\$ $/\$ $/\$

Theorem	cm2jt 9536	A lattice element that commutes with two others also commutes with their join. Theorem 4.2 of [Beran] p. 49.
$/\$ $/\$ $/\$ $/\$

Theorem	fh1 9537	Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular lattice elements commute, the triple is distributive. First of two parts. Theorem 5 of [Kalmbach] p. 25.


Theorem	fh2 9538	Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular lattice elements commute, the triple is distributive. Second of two parts. Theorem 5 of [Kalmbach] p. 25.


Theorem	fh3 9539	Variation of the Foulis-Holland Theorem.


Theorem	fh4 9540	Variation of the Foulis-Holland Theorem.


Quantum Logic Explorer axioms

Theorem	qlax1 9541	One of the equations showing is an ortholattice. (This corresponds to axiom "ax-1" in the Quantum Logic Explorer.)


Theorem	qlax2 9542	One of the equations showing is an ortholattice. (This corresponds to axiom "ax-2" in the Quantum Logic Explorer.)


Theorem	qlax3 9543	One of the equations showing is an ortholattice. (This corresponds to axiom "ax-3" in the Quantum Logic Explorer.)


Theorem	qlax4 9544	One of the equations showing is an ortholattice. (This corresponds to axiom "ax-4" in the Quantum Logic Explorer.)


Theorem	qlax5 9545	One of the equations showing is an ortholattice. (This corresponds to axiom "ax-5" in the Quantum Logic Explorer.)


Theorem	qlaxr1 9546	One of the conditions showing is an ortholattice. (This corresponds to axiom "ax-r1" in the Quantum Logic Explorer.)


Theorem	qlaxr2 9547	One of the conditions showing is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.)


Theorem	qlaxr4 9548	One of the conditions showing is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.)


Theorem	qlaxr5 9549	One of the conditions showing is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.)


Theorem	qlaxr3 9550	A variation of the orthomodular law, showing is an orthomodular lattice. (This corresponds to axiom "ax-r3" in the Quantum Logic Explorer.)