Nuprl Lemma : Wsucc_wf

[A:Type]. ∀[B:A ⟶ Type]. ∀[w:W(A;a.B[a])].  (Wsucc(A;a.B[a];w) ∈ ℙ)


Proof




Definitions occuring in Statement :  Wsucc: Wsucc(A;a.B[a];w) W: W(A;a.B[a]) uall: [x:A]. B[x] prop: so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T Wsucc: Wsucc(A;a.B[a];w) so_apply: x[s] so_lambda: λ2x.t[x] ext-eq: A ≡ B and: P ∧ Q subtype_rel: A ⊆B
Lemmas referenced :  ext-eq_wf W-ext pi1_wf W_wf unit_wf2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality lambdaEquality promote_hyp productElimination hypothesis_subsumption hypothesis functionEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache cumulativity universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[w:W(A;a.B[a])].    (Wsucc(A;a.B[a];w)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_14-AM-06_16_43
Last ObjectModification: 2015_12_26-PM-00_04_14

Theory : co-recursion


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