Nuprl Lemma : interval-type-ap-morph
∀[I,J,f,rho,u:Top]. ((u rho f) ~ dM-lift(J;I;f) u)
Proof
Definitions occuring in Statement :
interval-type: 𝕀,
cubical-type-ap-morph: (u a f),
dM-lift: dM-lift(I;J;f),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
interval-type: 𝕀,
cubical-type-ap-morph: (u a f),
constant-cubical-type: (X),
pi2: snd(t)
Lemmas referenced :
top_wf,
interval-presheaf-restriction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I,J,f,rho,u:Top]. ((u rho f) \msim{} dM-lift(J;I;f) u)
Date html generated:
2016_05_18-PM-01_59_49
Last ObjectModification:
2016_03_03-PM-02_25_34
Theory : cubical!type!theory
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