Nuprl Lemma : path-type-ap-morph
∀[X,A,a,b,I,J,f,alpha,u:Top]. ((u alpha f) ~ λK,g. (u K f ⋅ g))
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
cubical-type-ap-morph: (u a f),
nh-comp: g ⋅ f,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
path-type: (Path_A a b),
pathtype: Path(A),
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
all: ∀x:A. B[x],
top: Top,
cubical-fun: (A ⟶ B)
Lemmas referenced :
cubical_type_ap_morph_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A,a,b,I,J,f,alpha,u:Top]. ((u alpha f) \msim{} \mlambda{}K,g. (u K f \mcdot{} g))
Date html generated:
2017_01_10-AM-08_53_13
Last ObjectModification:
2016_12_19-AM-11_03_12
Theory : cubical!type!theory
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