Nuprl Lemma : fl-s-fl1
∀[I:fset(ℕ)]. ∀[x:names(I)]. (((x=1))<s> = (x=1) ∈ Point(face_lattice(I+x)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
fl1: (x=1),
face_lattice: face_lattice(I),
nc-s: s,
add-name: I+i,
names: names(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
names: names(I),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nc-s: s
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
face_lattice_wf,
add-name_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,
fl-morph-fl1,
nc-s_wf,
f-subset-add-name,
fl1_wf,
names-subtype,
iff_weakening_equal,
dM-to-FL-inc,
names_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
setElimination,
rename,
sqequalRule,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (((x=1))<s> = (x=1))
Date html generated:
2017_10_05-AM-01_14_01
Last ObjectModification:
2017_07_28-AM-09_31_19
Theory : cubical!type!theory
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