Nuprl Lemma : rename-one-iota
∀I:Cname List. ∀z,z1:Cname.
(iota(z) o rename-one-name(z;z1)) = iota(z1) ∈ name-morph(I;[z1 / I]) supposing (¬(z1 ∈ I)) ∧ (¬(z ∈ I))
Proof
Definitions occuring in Statement :
rename-one-name: rename-one-name(z1;z2),
name-comp: (f o g),
iota: iota(x),
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,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
cand: A c∧ B,
name-morph: name-morph(I;J),
rename-one-name: rename-one-name(z1;z2),
iota: iota(x),
name-comp: (f o g),
compose: f o g,
uext: uext(g),
ifthenelse: if b then t else f fi ,
btrue: tt,
nameset: nameset(L),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morphs-equal,
cons_wf,
coordinate_name_wf,
iota_wf,
not_wf,
l_member_wf,
list_wf,
name-comp_wf,
rename-one-name_wf,
name-morph_wf,
isname-nameset,
eq-cname_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nameset_wf,
set_subtype_base,
le_wf,
int_subtype_base,
nameset_subtype,
l_subset_right_cons_trivial,
nameset_subtype_extd-nameset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
equalitySymmetry,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_isectElimination,
productEquality,
applyEquality,
sqequalRule,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
functionExtensionality,
unionElimination,
equalityElimination,
equalityTransitivity,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
intEquality,
natural_numberEquality
Latex:
\mforall{}I:Cname List. \mforall{}z,z1:Cname.
(iota(z) o rename-one-name(z;z1)) = iota(z1) supposing (\mneg{}(z1 \mmember{} I)) \mwedge{} (\mneg{}(z \mmember{} I))
Date html generated:
2017_10_05-AM-10_09_20
Last ObjectModification:
2017_07_28-AM-11_17_11
Theory : cubical!sets
Home
Index