Nuprl Lemma : iota-identity
∀[I:Cname List]. ∀[x:Cname]. ∀[i:ℕ2]. (iota(x) o (x:=i)) = 1 ∈ name-morph(I;I) supposing ¬(x ∈ I)
Proof
Definitions occuring in Statement :
name-comp: (f o g),
iota: iota(x),
face-map: (x:=i),
id-morph: 1,
name-morph: name-morph(I;J),
coordinate_name: Cname,
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
name-morph: name-morph(I;J),
squash: ↓T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
face-map: (x:=i),
iota: iota(x),
name-comp: (f o g),
id-morph: 1,
uext: uext(g),
compose: f o g,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
id-morph_wf,
not_wf,
l_member_wf,
coordinate_name_wf,
int_seg_wf,
list_wf,
all_wf,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
extd-nameset_wf,
bool_wf,
eqtt_to_assert,
nameset_subtype_extd-nameset,
eq_int_wf,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
equalitySymmetry,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
natural_numberEquality,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_set_memberEquality,
lambdaEquality,
functionEquality,
applyEquality,
functionExtensionality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
hyp_replacement,
intEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[x:Cname]. \mforall{}[i:\mBbbN{}2]. (iota(x) o (x:=i)) = 1 supposing \mneg{}(x \mmember{} I)
Date html generated:
2017_10_05-AM-10_08_08
Last ObjectModification:
2017_07_28-AM-11_16_46
Theory : cubical!sets
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