### Nuprl Lemma : inv-rel_wf

`∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[finv:B ⟶ (A?)].  (inv-rel(A;B;f;finv) ∈ ℙ)`

Proof

Definitions occuring in Statement :  inv-rel: `inv-rel(A;B;f;finv)` uall: `∀[x:A]. B[x]` prop: `ℙ` unit: `Unit` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` universe: `Type`
Definitions unfolded in proof :  inv-rel: `inv-rel(A;B;f;finv)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  and_wf all_wf equal_wf unit_wf2
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality unionEquality hypothesis applyEquality inlEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].  \mforall{}[finv:B  {}\mrightarrow{}  (A?)].    (inv-rel(A;B;f;finv)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-03_54_57
Last ObjectModification: 2015_12_27-PM-01_24_36

Theory : general

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