Nuprl Lemma : cubical-path-ap-id-adjoin
∀[pth,x,Z:Top]. (((pth)p @ q)[x] ~ pth @ x)
Proof
Definitions occuring in Statement :
cubical-path-app: pth @ r,
csm-id-adjoin: [u],
cc-snd: q,
cc-fst: p,
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cubical-path-app: pth @ r,
cc-fst: p,
csm-ap-term: (t)s,
csm-id-adjoin: [u],
csm-id: 1(X),
csm-adjoin: (s;u),
csm-ap: (s)x,
cubicalpath-app: pth @ r,
cc-snd: q,
cubical-app: app(w; u),
pi1: fst(t),
pi2: snd(t),
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[pth,x,Z:Top]. (((pth)p @ q)[x] \msim{} pth @ x)
Date html generated:
2018_05_23-AM-09_35_26
Last ObjectModification:
2018_05_20-PM-06_37_17
Theory : cubical!type!theory
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