Nuprl Lemma : fl-deq_wf
∀[I:fset(ℕ)]. (Deq(F(I)) ∈ EqDecider(Point(face_lattice(I))))
Proof
Definitions occuring in Statement :
fl-deq: Deq(F(I)),
face_lattice: face_lattice(I),
lattice-point: Point(l),
fset: fset(T),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl-deq: Deq(F(I)),
deq: EqDecider(T),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rev_implies: P ⇐ Q
Lemmas referenced :
fset_wf,
nat_wf,
fl-eq_wf,
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-fl-eq,
assert_wf,
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
dependent_set_memberEquality,
lambdaEquality,
hypothesisEquality,
applyEquality,
instantiate,
productEquality,
cumulativity,
universeEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
independent_pairFormation,
productElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. (Deq(F(I)) \mmember{} EqDecider(Point(face\_lattice(I))))
Date html generated:
2016_05_18-PM-00_11_25
Last ObjectModification:
2015_12_28-PM-03_02_20
Theory : cubical!type!theory
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