### Nuprl Lemma : one-one_wf

`∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ].  (one-one(A;B;R) ∈ ℙ)`

Proof

Definitions occuring in Statement :  one-one: `one-one(A;B;R)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` one-one: `one-one(A;B;R)` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  all_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[A,B:Type].  \mforall{}[R:A  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].    (one-one(A;B;R)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-PM-03_55_54
Last ObjectModification: 2015_12_26-PM-06_55_25

Theory : relations2

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