Nuprl Lemma : lattice-fset-meet-singleton
∀[l:BoundedLattice]. ∀[x:Point(l)]. (/\({x}) = x ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice-fset-meet: /\(s),
bdd-lattice: BoundedLattice,
lattice-point: Point(l),
fset-singleton: {x},
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
fset-singleton: {x},
lattice-fset-meet: /\(s),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
bdd-lattice: BoundedLattice,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
cand: A c∧ B,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
reduce_cons_lemma,
reduce_nil_lemma,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
bounded-lattice-structure-subtype,
lattice-meet-1,
lattice-axioms_wf,
bounded-lattice-axioms_wf,
iff_weakening_equal,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
bdd-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
setElimination,
rename,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_pairFormation,
dependent_set_memberEquality,
productEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
instantiate,
cumulativity
Latex:
\mforall{}[l:BoundedLattice]. \mforall{}[x:Point(l)]. (/\mbackslash{}(\{x\}) = x)
Date html generated:
2020_05_20-AM-08_44_06
Last ObjectModification:
2017_07_28-AM-09_14_02
Theory : lattices
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