Nuprl Lemma : extend-name-morph-irrelevant
∀I,K:Cname List. ∀f:name-morph(I;K). (f = f[fresh-cname(I):=fresh-cname(K)] ∈ name-morph(I;K))
Proof
Definitions occuring in Statement :
extend-name-morph: f[z1:=z2],
name-morph: name-morph(I;J),
fresh-cname: fresh-cname(I),
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
extend-name-morph: f[z1:=z2],
nameset: nameset(L),
subtype_rel: A ⊆r B,
prop: ℙ,
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 ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
name-morph: name-morph(I;J)
Lemmas referenced :
name-morphs-equal,
eq-cname_wf,
fresh-cname_wf,
coordinate_name_wf,
not_wf,
l_member_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
fresh-cname-not-equal2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nameset_wf,
name-morph_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionExtensionality,
sqequalRule,
setElimination,
rename,
hypothesis,
applyEquality,
lambdaEquality,
setEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
because_Cache
Latex:
\mforall{}I,K:Cname List. \mforall{}f:name-morph(I;K). (f = f[fresh-cname(I):=fresh-cname(K)])
Date html generated:
2017_10_05-AM-10_08_46
Last ObjectModification:
2017_07_28-AM-11_17_01
Theory : cubical!sets
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