Nuprl Lemma : cubical-pi-subset
∀[X,phi,A,B,C:Top]. (X, phi.C ⊢ ΠA B ~ X.C ⊢ ΠA B)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
cubical-pi: ΠA B,
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
cube-context-adjoin: X.A,
cubical-pi: ΠA B,
context-subset: Gamma, phi,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
cubical-pi-family: cubical-pi-family(X;A;B;I;a),
uall: ∀[x:A]. B[x]
Lemmas referenced :
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality
Latex:
\mforall{}[X,phi,A,B,C:Top]. (X, phi.C \mvdash{} \mPi{}A B \msim{} X.C \mvdash{} \mPi{}A B)
Date html generated:
2017_01_10-AM-08_50_25
Last ObjectModification:
2016_12_11-PM-01_47_09
Theory : cubical!type!theory
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