Nuprl Lemma : name-morph-nil
∀[I:Cname List]. name-morph(I;[]) ≡ nameset(I) ⟶ ℕ2
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
nil: [],
list: T List,
int_seg: {i..j-},
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
all: ∀x:A. B[x],
implies: P ⇒ Q,
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
isname: isname(z),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bfalse: ff,
not: ¬A,
false: False,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morph_wf,
nil_wf,
coordinate_name_wf,
nameset_wf,
int_seg_wf,
list_wf,
extd-nameset-nil,
nsub2_subtype_extd-nameset,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
false_wf,
int_seg_subtype,
int_seg_cases,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
equal_wf,
extd-nameset_wf,
assert_wf,
bfalse_wf,
all_wf,
isname_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionEquality,
natural_numberEquality,
sqequalRule,
productElimination,
independent_pairEquality,
axiomEquality,
setElimination,
rename,
functionExtensionality,
applyEquality,
dependent_set_memberEquality,
lambdaFormation,
dependent_functionElimination,
unionElimination,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
voidElimination,
hypothesis_subsumption,
addEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}[I:Cname List]. name-morph(I;[]) \mequiv{} nameset(I) {}\mrightarrow{} \mBbbN{}2
Date html generated:
2017_10_05-AM-10_10_48
Last ObjectModification:
2017_07_28-AM-11_17_38
Theory : cubical!sets
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