Nuprl Lemma : fl-morph-fset-meet
∀[A,B:fset(ℕ)]. ∀[g:A ⟶ B]. ∀[x:fset(Point(face_lattice(B)))]. ((/\(x))<g> = /\(<g>"(x)) ∈ Point(face_lattice(A)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
face_lattice-deq: face_lattice-deq(),
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
fset-image: f"(s),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T,
lattice-fset-meet: /\(s),
lattice-point: Point(l)
Definitions unfolded in proof :
uall: ∀[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
Lemmas referenced :
lattice-hom-fset-meet,
face_lattice_wf,
bdd-distributive-lattice-subtype-bdd-lattice,
face_lattice-deq_wf,
fl-morph_wf,
fset_wf,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
names-hom_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
because_Cache,
universeIsType,
instantiate,
lambdaEquality_alt,
productEquality,
cumulativity,
isectEquality,
independent_isectElimination,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[A,B:fset(\mBbbN{})]. \mforall{}[g:A {}\mrightarrow{} B]. \mforall{}[x:fset(Point(face\_lattice(B)))]. ((/\mbackslash{}(x))<g> = /\mbackslash{}(<g>"(x)))
Date html generated:
2020_05_20-PM-01_44_22
Last ObjectModification:
2019_12_27-AM-00_17_21
Theory : cubical!type!theory
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