Nuprl Lemma : ss-eq_test

ss:SeparationSpace. ∀x,y,z,w:Point.  (y ≡  y ≡  w ≡  x ≡ w)


Proof




Definitions occuring in Statement :  ss-eq: x ≡ y ss-point: Point separation-space: SeparationSpace all: x:A. B[x] implies:  Q
Definitions unfolded in proof :  uall: [x:A]. B[x] prop: guard: {T} member: t ∈ T implies:  Q all: x:A. B[x]
Lemmas referenced :  separation-space_wf ss-point_wf ss-eq_wf ss-eq_transitivity ss-eq_inversion
Rules used in proof :  isectElimination hypothesis independent_functionElimination hypothesisEquality thin dependent_functionElimination sqequalHypSubstitution extract_by_obid introduction cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}ss:SeparationSpace.  \mforall{}x,y,z,w:Point.    (y  \mequiv{}  x  {}\mRightarrow{}  y  \mequiv{}  z  {}\mRightarrow{}  w  \mequiv{}  z  {}\mRightarrow{}  x  \mequiv{}  w)



Date html generated: 2016_11_08-AM-09_11_16
Last ObjectModification: 2016_10_31-AM-11_19_47

Theory : inner!product!spaces


Home Index