mmtheorems95 - 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 10601-10676

Color key:

Metamath Proof Explorer (1-8743)

Hilbert Space Explorer (8744-10676)

**Statement List for Metamath Proof Explorer -** 9401-9500 - Page 95 of 107
Type	Label	Description
Statement

Theorem	chj12 9401	A rearrangement of Hilbert lattice join.


Theorem	chj4 9402	Rearrangement of the join of 4 Hilbert lattice elements.


Theorem	chjjdir 9403	Hilbert lattice join distributes over itself.


Theorem	chdmm1t 9404	DeMorgan's law for meet in a Hilbert lattice.
$/\$

Theorem	chdmm2t 9405	DeMorgan's law for meet in a Hilbert lattice.
$/\$

Theorem	chdmm3t 9406	DeMorgan's law for meet in a Hilbert lattice.
$/\$

Theorem	chdmm4t 9407	DeMorgan's law for meet in a Hilbert lattice.
$/\$

Theorem	chdmj1t 9408	DeMorgan's law for join in a Hilbert lattice.
$/\$

Theorem	chdmj2t 9409	DeMorgan's law for join in a Hilbert lattice.
$/\$

Theorem	chdmj3t 9410	DeMorgan's law for join in a Hilbert lattice.
$/\$

Theorem	chdmj4t 9411	DeMorgan's law for join in a Hilbert lattice.
$/\$

Theorem	chjasst 9412	Associative law for Hilbert lattice join. From definition of lattice in [Kalmbach] p. 14.
$/\$ $/\$

Theorem	chj12t 9413	A rearrangement of Hilbert lattice join.
$/\$ $/\$

Theorem	chj4t 9414	Rearrangement of the join of 4 Hilbert lattice elements.
$/\$ $/\$ $/\$

Theorem	ledi 9415	An ortholattice is distributive in one ordering direction.


Theorem	ledir 9416	An ortholattice is distributive in one ordering direction.


Theorem	lejdi 9417	An ortholattice is distributive in one ordering direction (join version).


Theorem	lejdir 9418	An ortholattice is distributive in one ordering direction (join version).


Theorem	ledit 9419	An ortholattice is distributive in one ordering direction.
$/\$ $/\$

Span (cont.) and one-dimensional subspaces

Theorem	spansn0 9420	The span of the singleton of the zero vector is the zero subspace.


Theorem	span0 9421	The span of the empty set is the zero subspace. Remark 11.6.e of [Schechter] p. 276.


Theorem	elspan 9422	Membership in the span of a subset of Hilbert space.


Theorem	spanun 9423	The span of a union is the subspace sum of spans.


Theorem	spanunt 9424	The span of a union is the subspace sum of spans.
$/\$

Theorem	sshhococ 9425	The join of two Hilbert space subsets (not necessarily closed subspaces) equals the join of their closures (double orthocomplements).


Theorem	hne0 9426	Hilbert space has a nonzero vector iff it is not trivial.


Theorem	chsup0 9427	The supremum of the empty set.
$\/H$

Theorem	h1deot 9428	Membership in orthocomplement of 1-dimensional subspace.
$/\$

Theorem	h1det 9429	Membership in 1-dimensional subspace.
$/\$

Theorem	h1did 9430	A generating vector belongs to the 1-dimensional subspace it generates.


Theorem	h1dn0 9431	A non-zero vector generates a (non-zero) 1-dimensional subspace.
$/\$

Theorem	h1de2 9432	Membership in 1-dimensional subspace. All members are collinear with the generating vector.


Theorem	h1de2b 9433	Membership in 1-dimensional subspace. All members are collinear with the generating vector.


Theorem	h1de2bOLD 9434	Membership in 1-dimensional subspace. All members are collinear with the generating vector.


Theorem	h1de2ctlem 9435	Lemma for h1de2ct 9436.

Theorem	h1de2ct 9436	Membership in 1-dimensional subspace. All members are collinear with the generating vector.


Theorem	spansn 9437	The span of a singleton in Hilbert space equals its closure.


Theorem	elspansn 9438	Membership in the span of a singleton.


Theorem	spansnt 9439	The span of a singleton in Hilbert space equals its closure.


Theorem	spansncht 9440	The span of a Hilbert space singleton belongs to the Hilbert lattice.


Theorem	spansnsht 9441	The span of a Hilbert space singleton is a subspace.


Theorem	spansnch 9442	The span of a singleton in Hilbert space is a closed subspace.


Theorem	spansnid 9443	A vector belongs to the span of its singleton.


Theorem	spansnmul 9444	A scalar product with a vector belongs to the span of its singleton.
$/\$

Theorem	elspansnclt 9445	A member of a span of a singleton is a vector.
$/\$

Theorem	elspansnt 9446	Membership in the span of a singleton.


Theorem	elspansn2t 9447	Membership in the span of a singleton. All members are collinear with the generating vector.
$/\$ $/\$

Theorem	spansncol 9448	The singletons of collinear vectors have the same span.
$/\$ $/\$

Theorem	spansneleqi 9449	Membership relation implied by equality of spans.


Theorem	spansneleq 9450	Membership relation that implies equality of spans.
$/\$