Nuprl Lemma : dM-fl-all_wf
∀[I:fset(ℕ)]. ∀[phi:Point(face_lattice(I))]. ∀[z:Point(dM(I))]. (dM-fl-all(I;phi;z) ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
dM-fl-all: dM-fl-all(I;phi;z),
face_lattice: face_lattice(I),
dM: dM(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM-fl-all: dM-fl-all(I;phi;z),
names: names(I),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
lattice-point: Point(l),
record-select: r.x,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
btrue: tt,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
DeMorgan-algebra: DeMorganAlgebra,
guard: {T}
Lemmas referenced :
nat_wf,
fset_wf,
DeMorgan-algebra-axioms_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
DeMorgan-algebra-structure_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
bounded-lattice-structure_wf,
subtype_rel_set,
free-dist-lattice_wf,
dM_wf,
lattice-point_wf,
subtype_rel-equal,
f-subset-add-name,
add-name_wf,
face_lattice-point-subtype,
fl_all_wf,
face_lattice-deq_wf,
face_lattice_wf,
names-deq_wf,
union-deq_wf,
names_wf,
lattice-extend_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
because_Cache,
hypothesis,
lambdaEquality,
unionElimination,
setElimination,
rename,
hypothesisEquality,
applyEquality,
independent_isectElimination,
dependent_functionElimination,
instantiate,
productEquality,
cumulativity,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[phi:Point(face\_lattice(I))]. \mforall{}[z:Point(dM(I))].
(dM-fl-all(I;phi;z) \mmember{} Point(face\_lattice(I)))
Date html generated:
2016_05_18-PM-00_19_16
Last ObjectModification:
2016_03_25-PM-03_27_15
Theory : cubical!type!theory
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