Nuprl Lemma : lattice-meet-idempotent
∀[l:Lattice]. ∀[u:Point(l)]. (u ∧ u = u ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice: Lattice
,
lattice-meet: a ∧ b
,
lattice-point: Point(l)
,
uall: ∀[x:A]. B[x]
,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
lattice: Lattice
,
and: P ∧ Q
,
squash: ↓T
,
prop: ℙ
,
true: True
,
subtype_rel: A ⊆r B
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
Lemmas referenced :
lattice_properties,
lattice-point_wf,
lattice_wf,
lattice-meet_wf,
squash_wf,
true_wf,
lattice-structure_wf,
equal_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[l:Lattice]. \mforall{}[u:Point(l)]. (u \mwedge{} u = u)
Date html generated:
2017_10_05-AM-00_30_54
Last ObjectModification:
2017_07_28-AM-09_12_48
Theory : lattices
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