Nuprl Lemma : irr_face_wf
∀[I:fset(ℕ)]. ∀[as,bs:fset(names(I))]. (irr_face(I;as;bs) ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
irr_face: irr_face(I;as;bs),
face_lattice: face_lattice(I),
names: names(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
irr_face: irr_face(I;as;bs),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
all: ∀x:A. B[x],
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
lattice-fset-meet_wf,
face_lattice_wf,
decidable__equal_face_lattice,
lattice-point_wf,
fset-union_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,
face_lattice-deq_wf,
fset-image_wf,
names_wf,
names-deq_wf,
fl0_wf,
fl1_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[as,bs:fset(names(I))]. (irr\_face(I;as;bs) \mmember{} Point(face\_lattice(I)))
Date html generated:
2017_02_21-AM-10_32_57
Last ObjectModification:
2017_02_02-PM-03_08_32
Theory : cubical!type!theory
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