Nuprl Lemma : csm-path_comp
∀[G,H,A,a,b,cA,tau:Top]. ((path_comp(G;A;a;b;cA))tau ~ path_comp(H;(A)tau;(a)tau;(b)tau;(cA)tau))
Proof
Definitions occuring in Statement :
path_comp: path_comp,
csm-comp-structure: (cA)tau,
csm-ap-term: (t)s,
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
csm-comp-structure: (cA)tau,
path_comp: path_comp,
cc-snd: q,
cc-fst: p,
csm-ap-term: (t)s,
csm+: tau+,
csm-comp: G o F,
csm-ap: (s)x,
csm-ap-type: (AF)s,
csm-adjoin: (s;u),
compose: f o g,
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{}[G,H,A,a,b,cA,tau:Top]. ((path\_comp(G;A;a;b;cA))tau \msim{} path\_comp(H;(A)tau;(a)tau;(b)tau;(cA)tau))
Date html generated:
2018_05_23-AM-11_03_11
Last ObjectModification:
2018_05_20-PM-08_13_13
Theory : cubical!type!theory
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