Nuprl Lemma : name-comp_wf
∀[I,J,K:Cname List]. ∀[f:name-morph(I;J)]. ∀[g:name-morph(J;K)]. ((f o g) ∈ name-morph(I;K))
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],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
name-comp: (f o g),
all: ∀x:A. B[x],
compose: f o g,
uext: uext(g),
implies: P ⇒ Q,
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 ,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morph_wf,
list_wf,
coordinate_name_wf,
compose_wf,
nameset_wf,
extd-nameset_wf,
uext_wf,
isname_wf,
bool_wf,
eqtt_to_assert,
assert-isname,
equal_wf,
assert_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nameset_subtype_extd-nameset,
equal_functionality_wrt_subtype_rel2,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
functionExtensionality,
applyEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
lambdaEquality,
functionEquality
Latex:
\mforall{}[I,J,K:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[g:name-morph(J;K)]. ((f o g) \mmember{} name-morph(I;K))
Date html generated:
2017_10_05-AM-10_06_45
Last ObjectModification:
2017_07_28-AM-11_16_27
Theory : cubical!sets
Home
Index