Nuprl Lemma : face-type-ap-morph
∀[I,J,f,rho,u:Top]. ((u rho f) ~ (u)<f>)
Proof
Definitions occuring in Statement :
face-type: 𝔽,
cubical-type-ap-morph: (u a f),
fl-morph: <f>,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
cube-set-restriction: f(s),
face-presheaf: 𝔽,
pi2: snd(t),
constant-cubical-type: (X),
cubical-type-ap-morph: (u a f),
face-type: 𝔽,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
lemma_by_obid,
sqequalAxiom,
hypothesis,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I,J,f,rho,u:Top]. ((u rho f) \msim{} (u)<f>)
Date html generated:
2018_05_23-AM-09_19_29
Last ObjectModification:
2018_02_26-PM-05_54_59
Theory : cubical!type!theory
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