Nuprl Lemma : fl-morph-join
∀[A,B:fset(ℕ)]. ∀[g:A ⟶ B]. ∀[x,y:Point(face_lattice(B))]. ((x ∨ y)<g> = (x)<g> ∨ (y)<g> ∈ Point(face_lattice(A)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-join: a ∨ b,
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 :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bounded-lattice-hom: Hom(l1;l2),
and: P ∧ Q,
lattice-hom: Hom(l1;l2),
prop: ℙ,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
fl-morph_wf,
bounded-lattice-hom_wf,
face_lattice_wf,
bdd-distributive-lattice_wf,
equal_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,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
lambdaFormation,
equalitySymmetry,
productElimination,
equalityTransitivity,
dependent_functionElimination,
independent_functionElimination,
instantiate,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
isect_memberFormation,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A,B:fset(\mBbbN{})]. \mforall{}[g:A {}\mrightarrow{} B]. \mforall{}[x,y:Point(face\_lattice(B))]. ((x \mvee{} y)<g> = (x)<g> \mvee{} (y)<g>)
Date html generated:
2017_10_05-AM-01_14_35
Last ObjectModification:
2017_07_28-AM-09_31_40
Theory : cubical!type!theory
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