Nuprl Lemma : ccc-nset-transparent
∀K:Type. (CCCNSet(K) ⇒ Transparent(K))
Proof
Definitions occuring in Statement :
transparent-nset: Transparent(K),
ccc-nset: CCCNSet(K),
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
le: A ≤ B,
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
squash: ↓T,
less_than: a < b,
ge: i ≥ j ,
cand: A c∧ B,
decidable: Dec(P),
exists: ∃x:A. B[x],
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
contra-cc: CCC(T),
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
transparent-nset: Transparent(K),
and: P ∧ Q,
ccc-nset: CCCNSet(K),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
int_formula_prop_or_lemma,
intformor_wf,
istype-less_than,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
itermConstant_wf,
intformle_wf,
decidable__le,
istype-le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
decidable__lt,
nat_wf,
subtype_rel_transitivity,
less_than_wf,
int_subtype_base,
istype-int,
le_wf,
set_subtype_base,
equal-wf-base,
istype-universe,
ccc-nset_wf,
istype-nat
Rules used in proof :
equalityTransitivity,
Error :functionIsType,
Error :inrFormation_alt,
Error :unionIsType,
equalitySymmetry,
sqequalBase,
Error :equalityIstype,
Error :productIsType,
Error :dependent_set_memberEquality_alt,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
approximateComputation,
imageElimination,
Error :inlFormation_alt,
Error :dependent_pairFormation_alt,
unionElimination,
independent_functionElimination,
Error :inhabitedIsType,
setElimination,
unionEquality,
because_Cache,
independent_isectElimination,
natural_numberEquality,
intEquality,
applyEquality,
sqequalRule,
productEquality,
Error :lambdaEquality_alt,
dependent_functionElimination,
universeEquality,
instantiate,
hypothesisEquality,
isectElimination,
Error :universeIsType,
extract_by_obid,
introduction,
cut,
hypothesis,
independent_pairFormation,
rename,
thin,
productElimination,
sqequalHypSubstitution,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}K:Type. (CCCNSet(K) {}\mRightarrow{} Transparent(K))
Date html generated:
2019_06_20-PM-03_02_12
Last ObjectModification:
2019_06_13-AM-11_59_13
Theory : continuity
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