Nuprl Lemma : face_lattice-deq_wf
∀[I:fset(ℕ)]. (face_lattice-deq() ∈ EqDecider(Point(face_lattice(I))))
Proof
Definitions occuring in Statement :
face_lattice-deq: face_lattice-deq(),
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,
face_lattice: face_lattice(I),
subtype_rel: A ⊆r B,
face_lattice-deq: face_lattice-deq(),
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],
union-deq: union-deq(A;B;a;b),
bdd-distributive-lattice: BoundedDistributiveLattice,
guard: {T}
Lemmas referenced :
fl-point,
names_wf,
names-deq_wf,
fset_wf,
nat_wf,
deq-fset_wf,
strong-subtype-deq-subtype,
strong-subtype-set2,
all_wf,
not_wf,
fset-member_wf,
union-deq_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,
deq_wf,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
unionEquality,
because_Cache,
setEquality,
productEquality,
independent_isectElimination,
lambdaEquality,
functionEquality,
inlEquality,
inrEquality,
instantiate,
cumulativity,
universeEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. (face\_lattice-deq() \mmember{} EqDecider(Point(face\_lattice(I))))
Date html generated:
2016_05_18-PM-00_09_12
Last ObjectModification:
2015_12_28-PM-03_03_35
Theory : cubical!type!theory
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