Nuprl Lemma : csm-equiv-contr
∀[s,f,a:Top]. ((equiv-contr(f;a))s ~ equiv-contr((f)s;(a)s))
Proof
Definitions occuring in Statement :
equiv-contr: equiv-contr(f;a),
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
csm-ap-term: (t)s,
equiv-contr: equiv-contr(f;a),
cubical-snd: p.2,
cubical-app: app(w; u),
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{}[s,f,a:Top]. ((equiv-contr(f;a))s \msim{} equiv-contr((f)s;(a)s))
Date html generated:
2018_05_23-AM-09_43_36
Last ObjectModification:
2018_05_20-PM-06_42_50
Theory : cubical!type!theory
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