Nuprl Lemma : name-comp-assoc
∀[I,J,K,H:Cname List]. ∀[f:name-morph(I;J)]. ∀[g:name-morph(J;K)]. ∀[h:name-morph(K;H)].
(((f o g) o h) = (f o (g o h)) ∈ name-morph(I;H))
Proof
Definitions occuring in Statement :
name-comp: (f o g),
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
squash: ↓T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
name-comp: (f o g),
uext: uext(g),
compose: f o g,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
subtype_rel: A ⊆r B
Lemmas referenced :
name-comp_wf,
all_wf,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
extd-nameset_wf,
name-morph_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert-isname,
uext_wf,
not-assert-isname,
nsub2_subtype_extd-nameset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_set_memberEquality,
lambdaEquality,
functionEquality,
applyEquality,
functionExtensionality,
because_Cache,
isect_memberEquality,
axiomEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[I,J,K,H:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[g:name-morph(J;K)]. \mforall{}[h:name-morph(K;H)].
(((f o g) o h) = (f o (g o h)))
Date html generated:
2017_10_05-AM-10_06_56
Last ObjectModification:
2017_07_28-AM-11_16_30
Theory : cubical!sets
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