Nuprl Lemma : lattice-meet-le
∀l:Lattice. ∀a,b:Point(l). (a ∧ b ≤ a ∧ a ∧ b ≤ b)
Proof
Definitions occuring in Statement :
lattice-le: a ≤ b,
lattice: Lattice,
lattice-meet: a ∧ b,
lattice-point: Point(l),
all: ∀x:A. B[x],
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
greatest-lower-bound: greatest-lower-bound(T;x,y.R[x; y];a;b;c),
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
lattice: Lattice
Lemmas referenced :
lattice-meet-is-glb,
lattice-point_wf,
lattice_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairFormation,
isectElimination,
setElimination,
rename
Latex:
\mforall{}l:Lattice. \mforall{}a,b:Point(l). (a \mwedge{} b \mleq{} a \mwedge{} a \mwedge{} b \mleq{} b)
Date html generated:
2020_05_20-AM-08_25_38
Last ObjectModification:
2018_05_20-PM-10_10_45
Theory : lattices
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