Nuprl Lemma : fiber-comp-subset
∀[X,T,A,w,a,cT,cA,phi:Top]. (fiber-comp(X, phi;T;A;w;a;cT;cA) ~ fiber-comp(X;T;A;w;a;cT;cA))
Proof
Definitions occuring in Statement :
fiber-comp: fiber-comp(X;T;A;w;a;cT;cA),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
fiber-comp: fiber-comp(X;T;A;w;a;cT;cA),
sigma_comp: sigma_comp(cA;cB),
csm-comp-structure: (cA)tau,
csm-comp: G o F,
compose: f o g,
path_comp: path_comp,
cc-snd: q,
cc-fst: p,
csm-ap-term: (t)s,
csm+: tau+,
csm-id-adjoin: [u],
csm-ap-type: (AF)s,
csm-ap: (s)x,
csm-adjoin: (s;u),
csm-id: 1(X),
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{}[X,T,A,w,a,cT,cA,phi:Top]. (fiber-comp(X, phi;T;A;w;a;cT;cA) \msim{} fiber-comp(X;T;A;w;a;cT;cA))
Date html generated:
2017_01_10-AM-10_09_50
Last ObjectModification:
2017_01_03-PM-04_56_17
Theory : cubical!type!theory
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