Nuprl Lemma : fl-morph-1
∀[A,B:fset(ℕ)]. ∀[g:A ⟶ B]. ((1)<g> = 1 ∈ Point(face_lattice(A)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-1: 1,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
prop: ℙ
Lemmas referenced :
fl-morph_wf,
bounded-lattice-hom_wf,
face_lattice_wf,
bdd-distributive-lattice_wf,
equal_wf,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A,B:fset(\mBbbN{})]. \mforall{}[g:A {}\mrightarrow{} B]. ((1)<g> = 1)
Date html generated:
2017_10_05-AM-01_14_29
Last ObjectModification:
2017_07_28-AM-09_31_36
Theory : cubical!type!theory
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