Nuprl Lemma : lattice-join-idempotent
∀[l:Lattice]. ∀[u:Point(l)]. (u ∨ u = u ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice: Lattice,
lattice-join: 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-join_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 \mvee{} u = u)
Date html generated:
2020_05_20-AM-08_25_19
Last ObjectModification:
2017_07_28-AM-09_12_46
Theory : lattices
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