Nuprl Lemma : k-subtype_wf

`∀[k:ℕ]. ∀[A,B:ℕk ⟶ Type].  (A ⊆ B ∈ ℙ)`

Proof

Definitions occuring in Statement :  k-subtype: `A ⊆ B` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` k-subtype: `A ⊆ B` nat: `ℕ` so_lambda: `λ2x.t[x]` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  all_wf int_seg_wf subtype_rel_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename because_Cache hypothesis lambdaEquality applyEquality functionExtensionality hypothesisEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality isect_memberEquality

Latex:
\mforall{}[k:\mBbbN{}].  \mforall{}[A,B:\mBbbN{}k  {}\mrightarrow{}  Type].    (A  \msubseteq{}  B  \mmember{}  \mBbbP{})

Date html generated: 2018_05_21-PM-00_08_47
Last ObjectModification: 2017_10_18-PM-02_31_15

Theory : co-recursion

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