Nuprl Lemma : init0_wf
∀[a:ℕ ⟶ ℕ]. (init0(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
init0: init0(a),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
init0: init0(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
le_wf,
false_wf,
nat_wf,
equal-wf-T-base
Rules used in proof :
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
baseClosed,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (init0(a) \mmember{} \mBbbP{})
Date html generated:
2017_04_21-AM-11_22_21
Last ObjectModification:
2017_04_20-PM-03_42_53
Theory : continuity
Home
Index