Nuprl Lemma : swap-names_wf
∀[I:Cname List]. ∀[z1,z2:nameset(I)]. (swap-names(z1;z2) ∈ name-morph(I;I))
Proof
Definitions occuring in Statement :
swap-names: swap-names(z1;z2),
name-morph: name-morph(I;J),
nameset: nameset(L),
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,
swap-names: swap-names(z1;z2),
name-morph: name-morph(I;J),
nameset: nameset(L),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
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],
squash: ↓T,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
le: A ≤ B
Lemmas referenced :
nameset_wf,
list_wf,
coordinate_name_wf,
eq-cname_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
nameset_subtype_extd-nameset,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
l_member_wf,
extd-nameset_wf,
true_wf,
isname-nameset,
set_subtype_base,
le_wf,
int_subtype_base,
extd-nameset_subtype_base,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal-wf-base,
all_wf,
assert_wf,
isname_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
intEquality,
natural_numberEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
int_eqEquality,
voidEquality,
computeAll,
functionEquality,
functionExtensionality
Latex:
\mforall{}[I:Cname List]. \mforall{}[z1,z2:nameset(I)]. (swap-names(z1;z2) \mmember{} name-morph(I;I))
Date html generated:
2017_10_05-AM-10_09_04
Last ObjectModification:
2017_07_28-AM-11_17_04
Theory : cubical!sets
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