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


Home Index