Nuprl Lemma : path-type-subset-adjoin
∀[X,T,A,w,a,phi:Top]. ((X, phi.T ⊢ Path_A a w) ~ (X.T ⊢ Path_A a w))
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
context-subset: Gamma, phi,
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
path-type: (Path_A a b),
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
pathtype: Path(A),
member: t ∈ T,
top: Top
Lemmas referenced :
cubical-fun-subset-adjoin,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache
Latex:
\mforall{}[X,T,A,w,a,phi:Top]. ((X, phi.T \mvdash{} Path\_A a w) \msim{} (X.T \mvdash{} Path\_A a w))
Date html generated:
2018_05_23-AM-09_34_11
Last ObjectModification:
2018_05_20-PM-06_36_13
Theory : cubical!type!theory
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