Nuprl Lemma : FL-meet-0-1
∀[I:fset(ℕ)]. ∀[x:names(I)].
(((x=0) ∧ (x=1) = 0 ∈ Point(face_lattice(I))) ∧ ((x=1) ∧ (x=0) = 0 ∈ Point(face_lattice(I))))
Proof
Definitions occuring in Statement :
fl1: (x=1),
fl0: (x=0),
face_lattice: face_lattice(I),
names: names(I),
lattice-0: 0,
lattice-meet: a ∧ b,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
fl1: (x=1),
fl0: (x=0),
face_lattice: face_lattice(I),
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
fl-meet-0-1,
names_wf,
names-deq_wf,
equal_wf,
squash_wf,
true_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,
lattice-meet_wf,
lattice-join_wf,
fl1_wf,
fl0_wf,
iff_weakening_equal,
lattice_properties,
bdd-distributive-lattice-subtype-lattice,
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,
independent_pairFormation,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (((x=0) \mwedge{} (x=1) = 0) \mwedge{} ((x=1) \mwedge{} (x=0) = 0))
Date html generated:
2017_10_05-AM-01_11_00
Last ObjectModification:
2017_07_28-AM-09_29_59
Theory : cubical!type!theory
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