Nuprl Lemma : face-forall-subset
∀[Gamma,phi,xx:Top]. ((Gamma, xx ⊢ ∀ phi) ~ (Gamma ⊢ ∀ phi))
Proof
Definitions occuring in Statement :
face-forall: (∀ phi),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
face-forall: (∀ phi),
context-subset: Gamma, phi,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
cube_set_restriction_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[Gamma,phi,xx:Top]. ((Gamma, xx \mvdash{} \mforall{} phi) \msim{} (Gamma \mvdash{} \mforall{} phi))
Date html generated:
2018_05_23-AM-09_28_36
Last ObjectModification:
2018_05_20-PM-06_26_24
Theory : cubical!type!theory
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