Nuprl Lemma : path-type-subset
∀[X,A,a,b,phi:Top]. ((X, phi ⊢ Path_A a b) ~ (X ⊢ Path_A a b))
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
context-subset: Gamma, phi,
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]},
member: t ∈ T
Lemmas referenced :
pathtype-subset,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache
Latex:
\mforall{}[X,A,a,b,phi:Top]. ((X, phi \mvdash{} Path\_A a b) \msim{} (X \mvdash{} Path\_A a b))
Date html generated:
2018_05_23-AM-09_34_00
Last ObjectModification:
2018_05_20-PM-06_36_04
Theory : cubical!type!theory
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