Nuprl Lemma : csm-comp-op-to-comp-fun-sq
∀[Gamma,Delta,tau,cA:Top]. ((comp-op-to-comp-fun(cA))tau ~ comp-op-to-comp-fun(csm-composition(tau;cA)))
Proof
Definitions occuring in Statement :
csm-comp-structure: (cA)tau,
comp-op-to-comp-fun: comp-op-to-comp-fun(cA),
csm-composition: csm-composition(sigma;comp),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
csm-composition: csm-composition(sigma;comp),
comp-op-to-comp-fun: comp-op-to-comp-fun(cA),
csm-comp-structure: (cA)tau,
csm-ap: (s)x,
csm-comp: G o F,
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,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[Gamma,Delta,tau,cA:Top].
((comp-op-to-comp-fun(cA))tau \msim{} comp-op-to-comp-fun(csm-composition(tau;cA)))
Date html generated:
2016_05_19-AM-10_41_07
Last ObjectModification:
2016_05_01-PM-05_37_48
Theory : cubical!type!theory
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