Nuprl Lemma : csm-ap-comp-type-sq
∀[Gamma:CubicalSet]. ∀[Delta,Z,s1,s2:Top].  ∀A:{Gamma ⊢ _}. ((A)s2 o s1 ~ ((A)s2)s1)
Proof
Definitions occuring in Statement : 
csm-ap-type: (AF)s
, 
cubical-type: {X ⊢ _}
, 
csm-comp: G o F
, 
cubical-set: CubicalSet
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
all: ∀x:A. B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
cubical-type: {X ⊢ _}
, 
csm-ap-type: (AF)s
, 
csm-comp: G o F
, 
csm-ap: (s)x
, 
type-cat: TypeCat
, 
trans-comp: trans-comp(C;D;F;G;H;t1;t2)
, 
cat-comp: cat-comp(C)
, 
pi2: snd(t)
, 
compose: f o g
, 
member: t ∈ T
Lemmas referenced : 
cubical-set_wf, 
top_wf, 
cubical-type_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
productElimination, 
sqequalRule, 
hypothesis, 
lemma_by_obid, 
isectElimination, 
hypothesisEquality, 
because_Cache
Latex:
\mforall{}[Gamma:CubicalSet].  \mforall{}[Delta,Z,s1,s2:Top].    \mforall{}A:\{Gamma  \mvdash{}  \_\}.  ((A)s2  o  s1  \msim{}  ((A)s2)s1)
Date html generated:
2016_06_16-PM-05_39_47
Last ObjectModification:
2016_03_28-PM-09_46_48
Theory : cubical!sets
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