Nuprl Lemma : contra-dcc_wf
∀[T:Type]. (dCCC(T) ∈ ℙ)
Proof
Definitions occuring in Statement :
contra-dcc: dCCC(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
exists: ∃x:A. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
contra-dcc: dCCC(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
assert_wf,
bool_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
productEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (dCCC(T) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-03_00_19
Last ObjectModification:
2019_06_12-PM-08_02_19
Theory : continuity
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