Nuprl Lemma : decidable__equal-fl-point
∀[T:Type]. ∀eq:EqDecider(T). ∀x,y:Point(face-lattice(T;eq)). Dec(x = y ∈ Point(face-lattice(T;eq)))
Proof
Definitions occuring in Statement :
face-lattice: face-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
uimplies: b supposing a
Lemmas referenced :
deq_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
bounded-lattice-structure_wf,
subtype_rel_set,
face-lattice_wf,
lattice-point_wf,
face-lattice-constraints_wf,
fset-contains-none_wf,
fset-all_wf,
union-deq_wf,
fset-antichain_wf,
assert_wf,
and_wf,
decidable-equal-deq,
decidable__equal_union,
decidable__equal_fset,
fset_wf,
decidable__equal_set,
fl-point-sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalRule,
unionEquality,
hypothesisEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
lambdaEquality,
cumulativity,
applyEquality,
instantiate,
productEquality,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}x,y:Point(face-lattice(T;eq)). Dec(x = y)
Date html generated:
2020_05_20-AM-08_51_22
Last ObjectModification:
2016_01_19-PM-05_15_40
Theory : lattices
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