Nuprl Lemma : list-ss_wf
∀[ss:SeparationSpace]. (list(ss) ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
list-ss: list(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list-ss: list(ss),
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,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
so_apply: x[s],
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T ,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
subtype_rel: A ⊆r B,
exposed-it: exposed-it,
separation-space: SeparationSpace,
record+: record+,
record-select: r.x,
eq_atom: x =a y,
ss-sep: x # y,
ss-point: Point(ss),
true: True
Lemmas referenced :
mk-ss_wf,
list_wf,
ss-point_wf,
length_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
exists_wf,
int_seg_wf,
ss-sep_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
true_wf,
ss-sep-irrefl,
subtype_rel_self,
record-select_wf,
top_wf,
istype-atom,
not_wf,
all_wf,
or_wf,
istype-le,
istype-less_than,
int_eq_wf,
istype-true,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
because_Cache,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
sqequalRule,
int_eqReduceTrueSq,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
int_eqReduceFalseSq,
productIsType,
imageElimination,
functionIsType,
applyEquality,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
tokenEquality,
universeEquality,
setEquality,
functionEquality,
applyLambdaEquality,
functionExtensionality,
inlEquality_alt,
dependent_pairEquality_alt,
inrEquality_alt,
axiomEquality
Latex:
\mforall{}[ss:SeparationSpace]. (list(ss) \mmember{} SeparationSpace)
Date html generated:
2019_10_31-AM-07_27_10
Last ObjectModification:
2019_09_19-PM-04_12_51
Theory : constructive!algebra
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