Nuprl Lemma : name-morph-inv_wf
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (name-morph-inv(I;f) ∈ name-morph-range(f;I) ⟶ nameset(I))
Proof
Definitions occuring in Statement :
name-morph-inv: name-morph-inv(I;f),
name-morph-range: name-morph-range(f;I),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-inv: name-morph-inv(I;f),
name-morph-range: name-morph-range(f;I),
exists: ∃x:A. B[x],
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
coordinate_name: Cname,
int_upper: {i...},
nameset: nameset(L),
and: P ∧ Q,
all: ∀x:A. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
guard: {T},
bfalse: ff,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
cons: [a / b]
Lemmas referenced :
name-morph-range_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
band_wf,
isname_wf,
eq_int_wf,
extd-nameset_subtype_int,
nameset_wf,
list-subtype,
member_filter_2,
l_member_wf,
l_member-settype,
iff_transitivity,
assert_wf,
bool_wf,
eqtt_to_assert,
equal_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_eq_int,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
filter_wf5,
list-cases,
hd_wf,
member-implies-null-eq-bfalse,
null_nil_lemma,
btrue_wf,
btrue_neq_bfalse,
product_subtype_list,
length_cons_ge_one,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
hypothesis,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
applyEquality,
dependent_functionElimination,
setEquality,
dependent_set_memberEquality,
independent_functionElimination,
independent_pairFormation,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
productEquality,
intEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
computeAll,
promote_hyp,
hypothesis_subsumption
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)].
(name-morph-inv(I;f) \mmember{} name-morph-range(f;I) {}\mrightarrow{} nameset(I))
Date html generated:
2017_10_05-AM-10_06_02
Last ObjectModification:
2017_07_28-AM-11_16_14
Theory : cubical!sets
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