Nuprl Lemma : csm-contractible_comp
∀[X,H,cA,A,tau:Top]. ((contractible_comp(X;A;cA))tau ~ contractible_comp(H;(A)tau;(cA)tau))
Proof
Definitions occuring in Statement :
contractible_comp: contractible_comp(X;A;cA),
csm-comp-structure: (cA)tau,
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
contractible_comp: contractible_comp(X;A;cA),
top: Top,
csm-ap-type: (AF)s,
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,
csm-ap: (s)x,
cc-fst: p,
pi1: fst(t),
csm+: tau+,
csm-adjoin: (s;u),
csm-comp: G o F,
compose: f o g,
csm-comp-structure: (cA)tau,
csm-ap-term: (t)s,
cc-snd: q,
pi2: snd(t)
Lemmas referenced :
csm-sigma_comp2,
top_wf,
csm-pi_comp,
lifting-strict-spread,
strict4-spread,
csm-path_comp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
because_Cache,
baseClosed,
independent_isectElimination
Latex:
\mforall{}[X,H,cA,A,tau:Top]. ((contractible\_comp(X;A;cA))tau \msim{} contractible\_comp(H;(A)tau;(cA)tau))
Date html generated:
2017_01_10-AM-10_10_46
Last ObjectModification:
2016_12_24-AM-11_43_16
Theory : cubical!type!theory
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