Nuprl Lemma : fl_all-id
∀[I:fset(ℕ)]. ∀[i:{i:ℕ| ¬i ∈ I} ]. ∀[phi:Point(face_lattice(I))]. ((∀i.phi) = phi ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
fl_all: (∀i.phi),
face_lattice: face_lattice(I),
lattice-point: Point(l),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl_all: (∀i.phi),
squash: ↓T,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ
Lemmas referenced :
fl-all-hom_wf,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
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,
set_wf,
nat_wf,
not_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyLambdaEquality,
setElimination,
rename,
hypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
applyEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
instantiate,
productEquality,
cumulativity,
isect_memberEquality,
axiomEquality,
intEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\{i:\mBbbN{}| \mneg{}i \mmember{} I\} ]. \mforall{}[phi:Point(face\_lattice(I))]. ((\mforall{}i.phi) = phi)
Date html generated:
2017_10_05-AM-01_16_08
Last ObjectModification:
2017_07_28-AM-09_32_27
Theory : cubical!type!theory
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