Nuprl Lemma : lattice-le-order
∀l:Lattice. Order(Point(l);x,y.x ≤ y)
Proof
Definitions occuring in Statement :
lattice-le: a ≤ b,
lattice: Lattice,
lattice-point: Point(l),
order: Order(T;x,y.R[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
order: Order(T;x,y.R[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
lattice: Lattice,
cand: A c∧ B,
trans: Trans(T;x,y.E[x; y]),
implies: P ⇒ Q,
anti_sym: AntiSym(T;x,y.R[x; y]),
uimplies: b supposing a,
lattice-le: a ≤ b
Lemmas referenced :
lattice-point_wf,
lattice-le_wf,
lattice_wf,
lattice-le_weakening,
lattice-le_transitivity,
lattice_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
sqequalRule,
productElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}l:Lattice. Order(Point(l);x,y.x \mleq{} y)
Date html generated:
2020_05_20-AM-08_25_27
Last ObjectModification:
2015_12_28-PM-02_03_01
Theory : lattices
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