Nuprl Lemma : not-CCC-infinite
∀[A:Type]. ((∃f:A ⟶ ℕ. Surj(A;ℕ;f)) ⇒ (¬CCC(A)))
Proof
Definitions occuring in Statement :
contra-cc: CCC(T),
surject: Surj(A;B;f),
nat: ℕ,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
contra-cc: CCC(T),
prop: ℙ,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
contra-dcc: dCCC(T),
false: False,
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_wf,
istype-universe,
nat_wf,
surject_wf,
contra-cc_wf,
bool_wf,
istype-assert,
istype-nat,
not-d-CCC-infinite
Rules used in proof :
universeEquality,
instantiate,
Error :inhabitedIsType,
Error :functionIsTypeImplies,
dependent_functionElimination,
Error :lambdaEquality_alt,
voidElimination,
Error :universeIsType,
applyEquality,
Error :productIsType,
because_Cache,
Error :functionIsType,
sqequalRule,
hypothesis,
independent_functionElimination,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
thin,
Error :lambdaFormation_alt,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]. ((\mexists{}f:A {}\mrightarrow{} \mBbbN{}. Surj(A;\mBbbN{};f)) {}\mRightarrow{} (\mneg{}CCC(A)))
Date html generated:
2019_06_20-PM-03_00_58
Last ObjectModification:
2019_06_12-PM-09_01_56
Theory : continuity
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