Nuprl Lemma : csm-pathtype-comp
∀[G,A,cA,H,tau:Top]. ((pathtype-comp(G;A;cA))tau ~ pathtype-comp(H;(A)tau;(cA)tau))
Proof
Definitions occuring in Statement :
pathtype-comp: pathtype-comp(G;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 :
csm-comp-structure: (cA)tau,
pathtype-comp: pathtype-comp(G;A;cA),
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,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[G,A,cA,H,tau:Top]. ((pathtype-comp(G;A;cA))tau \msim{} pathtype-comp(H;(A)tau;(cA)tau))
Date html generated:
2018_05_23-AM-10_58_59
Last ObjectModification:
2018_05_20-PM-08_00_48
Theory : cubical!type!theory
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