Nuprl Lemma : dM-to-FL-is-hom
∀[I:fset(ℕ)]. (λz.dM-to-FL(I;z) ∈ Hom(free-DeMorgan-lattice(names(I);NamesDeq);face_lattice(I)))
Proof
Definitions occuring in Statement :
dM-to-FL: dM-to-FL(I;z),
face_lattice: face_lattice(I),
names-deq: NamesDeq,
names: names(I),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
bounded-lattice-hom: Hom(l1;l2),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM-to-FL: dM-to-FL(I;z),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq)
Lemmas referenced :
fset_wf,
nat_wf,
lattice-extend-is-hom,
names_wf,
union-deq_wf,
names-deq_wf,
face_lattice_wf,
face_lattice-deq_wf,
fl1_wf,
fl0_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
lambdaEquality,
because_Cache,
lambdaFormation,
unionElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. (\mlambda{}z.dM-to-FL(I;z) \mmember{} Hom(free-DeMorgan-lattice(names(I);NamesDeq);face\_lattice(I)))
Date html generated:
2019_11_04-PM-05_33_38
Last ObjectModification:
2018_08_21-PM-02_03_02
Theory : cubical!type!theory
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