Nuprl Lemma : csm-discrete-family
∀[A,B,s:Top]. ((discrete-family(A;a.B[a]))(s;q) ~ discrete-family(A;a.B[a]))
Proof
Definitions occuring in Statement :
discrete-family: discrete-family(A;a.B[a]),
csm-adjoin: (s;u),
cc-snd: q,
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
pi2: snd(t),
csm-ap: (s)x,
csm-adjoin: (s;u),
cc-snd: q,
csm-ap-type: (AF)s,
discrete-family: discrete-family(A;a.B[a]),
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
hypothesis,
extract_by_obid,
introduction,
cut,
because_Cache,
sqequalRule,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B,s:Top]. ((discrete-family(A;a.B[a]))(s;q) \msim{} discrete-family(A;a.B[a]))
Date html generated:
2017_02_21-AM-10_44_57
Last ObjectModification:
2017_02_16-PM-03_22_17
Theory : cubical!type!theory
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