Nuprl Lemma : ccc-nset-weakly-decidable
∀K:Type. (CCCNSet(K) ⇒ WD(K))
Proof
Definitions occuring in Statement :
weakly-decidable-nset: WD(K),
ccc-nset: CCCNSet(K),
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
less_than': less_than'(a;b),
respects-equality: respects-equality(S;T),
cand: A c∧ B,
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
nat: ℕ,
sq_type: SQType(T),
guard: {T},
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
decidable: Dec(P),
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
ccc-nset: CCCNSet(K),
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
weakly-decidable-nset: WD(K),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
subtract_nat_wf,
add_nat_wf,
subtype-respects-equality,
subtype_rel_set,
equal_wf,
ccc-nset-minimum,
ccc-nset-remove1,
int_term_value_add_lemma,
itermAdd_wf,
nat_properties,
primrec-wf2,
not_wf,
lelt_wf,
equal-wf-base,
le_wf,
istype-nat,
less_than_wf,
contra-cc_wf,
subtype_rel_wf,
nat_wf,
subtype_rel_transitivity,
subtype_rel_self,
istype-less_than,
istype-le,
decidable__lt,
decidable__le,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
subtract_wf,
decidable__equal_int,
int_seg_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
full-omega-unsat,
int_seg_properties,
istype-universe,
ccc-nset_wf
Rules used in proof :
sqequalBase,
Error :inrFormation_alt,
baseClosed,
imageMemberEquality,
Error :inlFormation_alt,
setEquality,
Error :equalityIstype,
addEquality,
Error :setIsType,
imageElimination,
unionEquality,
productEquality,
functionEquality,
intEquality,
Error :inhabitedIsType,
Error :functionIsType,
hypothesis_subsumption,
Error :productIsType,
Error :dependent_set_memberEquality_alt,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
applyEquality,
unionElimination,
cumulativity,
voidElimination,
Error :isect_memberEquality_alt,
dependent_functionElimination,
int_eqEquality,
Error :lambdaEquality_alt,
Error :dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
rename,
setElimination,
sqequalRule,
productElimination,
universeEquality,
instantiate,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
Error :universeIsType,
independent_pairFormation,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}K:Type. (CCCNSet(K) {}\mRightarrow{} WD(K))
Date html generated:
2019_06_20-PM-03_02_00
Last ObjectModification:
2019_06_13-PM-01_19_13
Theory : continuity
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