Nuprl Lemma : dM-to-FL-opp
∀[I:fset(ℕ)]. ∀[x:names(I)]. (dM-to-FL(I;<1-x>) = (x=0) ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
dM-to-FL: dM-to-FL(I;z),
fl0: (x=0),
face_lattice: face_lattice(I),
dM_opp: <1-x>,
names: names(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM-to-FL: dM-to-FL(I;z),
dM_opp: <1-x>,
dmopp: <1-i>,
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],
implies: P ⇒ Q,
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
names_wf,
fset_wf,
nat_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,
union-deq_wf,
names-deq_wf,
face_lattice-deq_wf,
fl1_wf,
fl0_wf,
squash_wf,
true_wf,
lattice-extend-dl-inc,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
independent_isectElimination,
unionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
inrEquality,
natural_numberEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (dM-to-FL(I;ə-x>) = (x=0))
Date html generated:
2019_11_04-PM-05_33_30
Last ObjectModification:
2018_08_21-PM-02_02_55
Theory : cubical!type!theory
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