Nuprl Lemma : fl-deq_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (fl-deq(T;eq) ∈ EqDecider(Point(face-lattice(T;eq))))
Proof
Definitions occuring in Statement :
fl-deq: fl-deq(T;eq),
face-lattice: face-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
fl-deq: fl-deq(T;eq),
and: P ∧ Q,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
bdd-distributive-lattice: BoundedDistributiveLattice,
guard: {T}
Lemmas referenced :
fl-point,
deq_wf,
deq-fset_wf,
fset_wf,
union-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set2,
all_wf,
not_wf,
fset-member_wf,
deq_functionality_wrt_ext-eq,
lattice-point_wf,
face-lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
assert_wf,
fset-antichain_wf,
ext-eq_inversion,
subtype_rel_weakening
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
universeEquality,
unionEquality,
cumulativity,
because_Cache,
setEquality,
productEquality,
independent_isectElimination,
lambdaEquality,
functionEquality,
inlEquality,
inrEquality,
instantiate
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (fl-deq(T;eq) \mmember{} EqDecider(Point(face-lattice(T;eq))))
Date html generated:
2020_05_20-AM-08_51_18
Last ObjectModification:
2015_12_28-PM-01_57_51
Theory : lattices
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