Nuprl Lemma : d-CCC-finite
∀[T:Type]. (finite(T) ⇒ dCCC(T))
Proof
Definitions occuring in Statement :
contra-dcc: dCCC(T),
finite: finite(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
pi1: fst(t),
decidable: Dec(P),
prop: ℙ,
false: False,
not: ¬A,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
exists: ∃x:A. B[x],
or: P ∨ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
contra-dcc: dCCC(T),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_witness,
pi1_wf,
nat_wf,
istype-universe,
finite_wf,
bool_wf,
istype-assert,
istype-nat,
istype-le,
istype-void,
finite-decidable-inhabited,
decidable__assert,
decidable__not,
assert_wf,
not_wf,
decidable-exists-finite
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
Error :equalityIstype,
Error :dependent_pairEquality_alt,
productElimination,
Error :inhabitedIsType,
functionExtensionality,
universeEquality,
instantiate,
Error :productIsType,
Error :functionIsType,
voidElimination,
independent_pairFormation,
natural_numberEquality,
Error :dependent_set_memberEquality_alt,
Error :dependent_pairFormation_alt,
unionElimination,
rename,
because_Cache,
dependent_functionElimination,
Error :universeIsType,
applyEquality,
Error :lambdaEquality_alt,
sqequalRule,
independent_functionElimination,
Error :lambdaFormation_alt,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}[T:Type]. (finite(T) {}\mRightarrow{} dCCC(T))
Date html generated:
2019_06_20-PM-03_00_27
Last ObjectModification:
2019_06_12-PM-08_08_34
Theory : continuity
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