Nuprl Lemma : lattice-fset-join-singleton
∀[l:BoundedLattice]. ∀[x:Point(l)]. (\/({x}) = x ∈ Point(l))
Proof
Definitions occuring in Statement :
lattice-fset-join: \/(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-join: \/(s),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
bdd-lattice: BoundedLattice,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
guard: {T},
bounded-lattice-axioms: bounded-lattice-axioms(l)
Lemmas referenced :
reduce_cons_lemma,
reduce_nil_lemma,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
and_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
bdd-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
setElimination,
rename,
productElimination,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
cumulativity,
independent_isectElimination
Latex:
\mforall{}[l:BoundedLattice]. \mforall{}[x:Point(l)]. (\mbackslash{}/(\{x\}) = x)
Date html generated:
2020_05_20-AM-08_43_46
Last ObjectModification:
2015_12_28-PM-02_01_26
Theory : lattices
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