### Nuprl Lemma : p-graph_wf2

`∀[A:Type]. ∀[f:A ⟶ (A + Top)].  (p-graph(A;f) ∈ A ⟶ A ⟶ ℙ)`

Proof

Definitions occuring in Statement :  p-graph: `p-graph(A;f)` uall: `∀[x:A]. B[x]` top: `Top` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` universe: `Type`
Definitions unfolded in proof :  p-graph: `p-graph(A;f)` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` cand: `A c∧ B` subtype_rel: `A ⊆r B` uimplies: `b supposing a` top: `Top`
Lemmas referenced :  assert_wf can-apply_wf subtype_rel_union top_wf equal_wf do-apply_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaEquality productEquality extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality functionExtensionality applyEquality hypothesis because_Cache independent_isectElimination isect_memberEquality voidElimination voidEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality unionEquality universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[f:A  {}\mrightarrow{}  (A  +  Top)].    (p-graph(A;f)  \mmember{}  A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2018_05_21-PM-07_36_33
Last ObjectModification: 2017_07_26-PM-05_10_34

Theory : general

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