Nuprl Lemma : CCC-compact
∀K:Type. (CCCNSet(K) ⇒ compact-type(K))
Proof
Definitions occuring in Statement :
compact-type: compact-type(T),
ccc-nset: CCCNSet(K),
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
compact-type: compact-type(T),
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
or: P ∨ Q,
exists: ∃x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
not: ¬A,
true: True,
false: False,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
CCC-omni,
not_wf,
assert_wf,
decidable__not,
decidable__assert,
eqtt_to_assert,
istype-true,
istype-void,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
bfalse_wf,
btrue_wf,
iff_imp_equal_bool,
ccc-nset_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
lambdaEquality_alt,
isectElimination,
applyEquality,
universeIsType,
because_Cache,
unionElimination,
inlFormation_alt,
productElimination,
dependent_pairFormation_alt,
inhabitedIsType,
equalityElimination,
independent_isectElimination,
natural_numberEquality,
voidElimination,
functionIsType,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
inrFormation_alt,
independent_pairFormation,
productIsType,
universeEquality
Latex:
\mforall{}K:Type. (CCCNSet(K) {}\mRightarrow{} compact-type(K))
Date html generated:
2019_10_15-AM-10_47_07
Last ObjectModification:
2019_06_20-AM-10_22_17
Theory : basic
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