Nuprl Lemma : rename-one-same
∀I:Cname List. ∀z:Cname. rename-one-name(z;z) = 1 ∈ name-morph([z / I];[z / I]) supposing ¬(z ∈ I)
Proof
Definitions occuring in Statement :
rename-one-name: rename-one-name(z1;z2),
id-morph: 1,
name-morph: name-morph(I;J),
coordinate_name: Cname,
l_member: (x ∈ l),
cons: [a / b],
list: T List,
uimplies: b supposing a,
all: ∀x:A. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
id-morph: 1,
rename-one-name: rename-one-name(z1;z2),
nameset: nameset(L),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
bfalse: ff,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
not_wf,
l_member_wf,
coordinate_name_wf,
list_wf,
cons_wf,
rename-one-name_wf,
id-morph_wf,
name-morph_wf,
eq-cname_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
subtype_base_sq,
set_subtype_base,
le_wf,
int_subtype_base,
cons_member,
nameset_subtype_extd-nameset,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
nameset_wf,
name-morphs-equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
functionExtensionality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
instantiate,
cumulativity,
intEquality,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination,
inlFormation,
dependent_set_memberEquality,
dependent_pairFormation,
promote_hyp,
voidElimination
Latex:
\mforall{}I:Cname List. \mforall{}z:Cname. rename-one-name(z;z) = 1 supposing \mneg{}(z \mmember{} I)
Date html generated:
2017_10_05-AM-10_09_15
Last ObjectModification:
2017_07_28-AM-11_17_09
Theory : cubical!sets
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