Nuprl Lemma : csm-fiber-comp-sq
∀[G,A,T,a,cA,cT,H,s,f:Top]. ((fiber-comp(G;T;A;f;a;cT;cA))s ~ fiber-comp(H;(T)s;(A)s;(f)s;(a)s;(cT)s;(cA)s))
Proof
Definitions occuring in Statement :
fiber-comp: fiber-comp(X;T;A;w;a;cT;cA),
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],
fiber-comp: fiber-comp(X;T;A;w;a;cT;cA),
member: t ∈ T,
top: Top,
csm-ap-term: (t)s,
cc-fst: p,
csm+: tau+,
csm-ap: (s)x,
cc-snd: q,
csm-ap-type: (AF)s,
csm-comp: G o F,
csm-adjoin: (s;u),
pi1: fst(t),
compose: f o g,
pi2: snd(t),
csm-comp-structure: (cA)tau,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
top_wf,
csm-sigma_comp,
csm-path_comp,
csm-cubical-app,
lifting-strict-spread,
strict4-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination
Latex:
\mforall{}[G,A,T,a,cA,cT,H,s,f:Top].
((fiber-comp(G;T;A;f;a;cT;cA))s \msim{} fiber-comp(H;(T)s;(A)s;(f)s;(a)s;(cT)s;(cA)s))
Date html generated:
2017_01_10-AM-10_09_35
Last ObjectModification:
2016_12_24-PM-01_22_48
Theory : cubical!type!theory
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