Nuprl Lemma : cubical-fun-subset
∀[G,phi,T,A:Top]. ((G, phi ⊢ T ⟶ A) ~ (G ⊢ T ⟶ A))
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
cubical-fun: (A ⟶ B),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
all: ∀x:A. B[x],
cubical-fun-family: cubical-fun-family(X; A; B; I; a),
context-subset: Gamma, phi,
cubical-fun: (A ⟶ B)
Lemmas referenced :
cube_set_restriction_pair_lemma,
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
isectElimination,
sqequalAxiom,
introduction,
isect_memberFormation,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[G,phi,T,A:Top]. ((G, phi \mvdash{} T {}\mrightarrow{} A) \msim{} (G \mvdash{} T {}\mrightarrow{} A))
Date html generated:
2016_05_19-AM-08_27_20
Last ObjectModification:
2016_04_13-PM-01_01_59
Theory : cubical!type!theory
Home
Index