Nuprl Lemma : face-map_wf
∀[L:Cname List]. ∀[x:Cname]. ∀[p:ℕ2]. ((x:=p) ∈ name-morph([x / L];L))
Proof
Definitions occuring in Statement :
face-map: (x:=i),
name-morph: name-morph(I;J),
coordinate_name: Cname,
cons: [a / b],
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-map: (x:=i),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
nequal: a ≠ b ∈ T ,
squash: ↓T,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
decidable: Dec(P),
isname: isname(z),
le_int: i ≤z j,
lt_int: i <z j,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_seg_wf,
coordinate_name_wf,
list_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nsub2_subtype_extd-nameset,
l_member_wf,
nameset_subtype_extd-nameset,
cons_member,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
nameset_wf,
cons_wf,
nil_wf,
decidable__equal_int,
int_subtype_base,
false_wf,
int_seg_subtype,
int_seg_cases,
intformless_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
assert_wf,
isname_wf,
extd-nameset_wf,
extd-nameset_subtype_base,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
natural_numberEquality,
isect_memberEquality,
hypothesisEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
applyEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
int_eqEquality,
intEquality,
voidEquality,
independent_pairFormation,
computeAll,
hypothesis_subsumption,
addEquality,
functionEquality,
functionExtensionality
Latex:
\mforall{}[L:Cname List]. \mforall{}[x:Cname]. \mforall{}[p:\mBbbN{}2]. ((x:=p) \mmember{} name-morph([x / L];L))
Date html generated:
2017_10_05-AM-10_06_24
Last ObjectModification:
2017_07_28-AM-11_16_20
Theory : cubical!sets
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