Nuprl Lemma : fiber-member-fiber-point
∀[X,a,b:Top]. (fiber-member(fiber-point(a;b)) ~ (a)1(X))
Proof
Definitions occuring in Statement :
fiber-member: fiber-member(p),
fiber-point: fiber-point(t;c),
csm-ap-term: (t)s,
csm-id: 1(X),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
fiber-point: fiber-point(t;c),
fiber-member: fiber-member(p),
cubical-pair: cubical-pair(u;v),
cubical-fst: p.1,
pi1: fst(t),
csm-id: 1(X),
csm-ap-term: (t)s,
csm-ap: (s)x,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,a,b:Top]. (fiber-member(fiber-point(a;b)) \msim{} (a)1(X))
Date html generated:
2018_05_23-AM-09_40_52
Last ObjectModification:
2018_05_20-PM-06_41_10
Theory : cubical!type!theory
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