### Nuprl Lemma : rleq2_wf

`∀[x,y:ℕ+ ⟶ ℤ].  (rleq2(x;y) ∈ ℙ)`

Proof

Definitions occuring in Statement :  rleq2: `rleq2(x;y)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rleq2: `rleq2(x;y)` so_lambda: `λ2x.t[x]` nat_plus: `ℕ+` int_upper: `{i...}` le: `A ≤ B` and: `P ∧ Q` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  all_wf nat_plus_wf exists_wf int_upper_wf le_wf subtract_wf less_than_transitivity1 less_than_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality because_Cache setElimination rename hypothesisEquality multiplyEquality minusEquality natural_numberEquality applyEquality dependent_set_memberEquality productElimination independent_isectElimination axiomEquality equalityTransitivity equalitySymmetry functionEquality intEquality isect_memberEquality

Latex:
\mforall{}[x,y:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].    (rleq2(x;y)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-07_15_10
Last ObjectModification: 2015_12_28-AM-00_42_43

Theory : reals

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