Nuprl Lemma : initF_wf
∀[a:ℕ ⟶ 𝔹]. (initF(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
initF: initF(a),
nat: ℕ,
bool: 𝔹,
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,
initF: initF(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
le_wf,
false_wf,
nat_wf,
bool_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{} \mBbbB{}]. (initF(a) \mmember{} \mBbbP{})
Date html generated:
2017_04_21-AM-11_22_09
Last ObjectModification:
2017_04_20-PM-03_41_40
Theory : continuity
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