Nuprl Lemma : trans_comp_ap_lemma
∀A,t2,t1,H,G,F,D,C:Top. (t1 o t2 A ~ cat-comp(D) (F A) (G A) (H A) (t1 A) (t2 A))
Proof
Definitions occuring in Statement :
trans-comp: t1 o t2,
functor-ob: ob(F),
cat-comp: cat-comp(C),
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
trans-comp: t1 o t2,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
ap_mk_nat_trans_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation
Latex:
\mforall{}A,t2,t1,H,G,F,D,C:Top. (t1 o t2 A \msim{} cat-comp(D) (F A) (G A) (H A) (t1 A) (t2 A))
Date html generated:
2020_05_20-AM-07_51_42
Last ObjectModification:
2017_01_11-PM-01_57_55
Theory : small!categories
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