Nuprl Lemma : CCC-nat2K-implies-CCC-K
∀[K:Type]. (CCC(ℕ ⟶ K) ⇒ CCC(K))
Proof
Definitions occuring in Statement :
contra-cc: CCC(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
false: False,
not: ¬A,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
prop: ℙ,
subtype_rel: A ⊆r B,
member: t ∈ T,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
contra-cc: CCC(T),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-le,
istype-void,
istype-universe,
nat_wf,
contra-cc_wf,
subtype_rel_self,
istype-nat
Rules used in proof :
Error :dependent_pairFormation_alt,
productElimination,
independent_functionElimination,
Error :inhabitedIsType,
voidElimination,
independent_pairFormation,
natural_numberEquality,
Error :dependent_set_memberEquality_alt,
Error :lambdaEquality_alt,
dependent_functionElimination,
functionEquality,
universeEquality,
isectElimination,
sqequalHypSubstitution,
instantiate,
thin,
applyEquality,
because_Cache,
Error :productIsType,
hypothesisEquality,
Error :universeIsType,
hypothesis,
extract_by_obid,
introduction,
cut,
Error :functionIsType,
sqequalRule,
Error :lambdaFormation_alt,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:Type]. (CCC(\mBbbN{} {}\mrightarrow{} K) {}\mRightarrow{} CCC(K))
Date html generated:
2019_06_20-PM-03_01_14
Last ObjectModification:
2019_06_14-PM-04_16_00
Theory : continuity
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