Nuprl Lemma : fl_all-implies-instance
∀[I:fset(ℕ)]. ∀[x:Point(dM(I))]. ∀[i:ℕ]. ∀[v:Point(face_lattice(I+i))].
(((∀i.v) = 1 ∈ Point(face_lattice(I))) ⇒ ((v)<(i/x)> = 1 ∈ Point(face_lattice(I))))
Proof
Definitions occuring in Statement :
fl_all: (∀i.phi),
fl-morph: <f>,
face_lattice: face_lattice(I),
nc-p: (i/z),
add-name: I+i,
dM: dM(I),
lattice-1: 1,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
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,
DeMorgan-algebra: DeMorganAlgebra,
guard: {T},
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top,
cand: A c∧ B,
or: P ∨ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
names: names(I),
nat: ℕ,
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
bfalse: ff,
false: False,
lattice-1: 1,
record-select: r.x,
face_lattice: face_lattice(I),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
eq_atom: x =a y,
fset-singleton: {x},
cons: [a / b]
Lemmas referenced :
equal_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,
fl_all_wf,
lattice-1_wf,
bdd-distributive-lattice_wf,
add-name_wf,
nat_wf,
dM_wf,
DeMorgan-algebra-structure_wf,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
DeMorgan-algebra-axioms_wf,
fset_wf,
face_lattice-induction,
fl-morph_wf,
nc-p_wf,
bounded-lattice-hom_wf,
sq_stable__all,
sq_stable__equal,
squash_wf,
true_wf,
fl-morph-0,
iff_weakening_equal,
fl_all-0,
lattice-0_wf,
fl-morph-1,
fl0_wf,
fl1_wf,
names_wf,
fl_all-join,
fl-morph-join,
face_lattice-1-join-irreducible,
fl_all-meet,
fl-morph-meet,
lattice-meet-eq-1,
bdd-distributive-lattice-subtype-bdd-lattice,
fl_all-fl0,
eq_int_wf,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
face-lattice-0-not-1,
face_lattice-point-subtype,
f-subset-add-name,
fl_all-fl1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
because_Cache,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
setElimination,
rename,
functionEquality,
equalityTransitivity,
equalitySymmetry,
imageElimination,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
unionElimination,
inlFormation,
inrFormation,
intEquality,
impliesFunctionality,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. \mforall{}[i:\mBbbN{}]. \mforall{}[v:Point(face\_lattice(I+i))].
(((\mforall{}i.v) = 1) {}\mRightarrow{} ((v)<(i/x)> = 1))
Date html generated:
2017_10_05-AM-01_16_58
Last ObjectModification:
2017_07_28-AM-09_32_48
Theory : cubical!type!theory
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