Nuprl Lemma : csm-comp-sq
∀[A,B,C,F,G:Top]. (G o F ~ λA,x. (G A (F A x)))
Proof
Definitions occuring in Statement :
csm-comp: G o 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,
csm-comp: G o F,
trans-comp: t1 o t2,
mk-nat-trans: x |→ T[x],
cat-comp: cat-comp(C),
pi2: snd(t),
type-cat: TypeCat,
compose: f o g
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[A,B,C,F,G:Top]. (G o F \msim{} \mlambda{}A,x. (G A (F A x)))
Date html generated:
2018_05_23-PM-06_28_31
Last ObjectModification:
2018_05_18-AM-10_31_08
Theory : cubical!sets
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