### Nuprl Lemma : or-to-and-by-cases

`∀[X:ℙ]. (Dec(X) `` (∀[P,Q:ℙ].  ((P `` X) `` (Q `` (¬X)) `` {P ∨ Q `⇐⇒` (X `` P) ∧ ((¬X) `` Q)})))`

Proof

Definitions occuring in Statement :  decidable: `Dec(P)` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` iff: `P `⇐⇒` Q` not: `¬A` implies: `P `` Q` or: `P ∨ Q` and: `P ∧ Q`
Definitions unfolded in proof :  guard: `{T}` decidable: `Dec(P)` uall: `∀[x:A]. B[x]` implies: `P `` Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` or: `P ∨ Q` not: `¬A` false: `False` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q`
Lemmas referenced :  and_wf or_wf not_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation independent_pairFormation sqequalHypSubstitution unionElimination thin hypothesis independent_functionElimination voidElimination hypothesisEquality cut lemma_by_obid isectElimination productElimination inlFormation inrFormation functionEquality universeEquality

Latex:
\mforall{}[X:\mBbbP{}].  (Dec(X)  {}\mRightarrow{}  (\mforall{}[P,Q:\mBbbP{}].    ((P  {}\mRightarrow{}  X)  {}\mRightarrow{}  (Q  {}\mRightarrow{}  (\mneg{}X))  {}\mRightarrow{}  \{P  \mvee{}  Q  \mLeftarrow{}{}\mRightarrow{}  (X  {}\mRightarrow{}  P)  \mwedge{}  ((\mneg{}X)  {}\mRightarrow{}  Q)\})))

Date html generated: 2016_05_13-PM-03_17_22
Last ObjectModification: 2016_01_06-PM-05_20_15

Theory : core_2

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