Nuprl Lemma : rel_or_idempotent

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  R ∨ ⇐⇒ R


Proof




Definitions occuring in Statement :  rel_equivalent: R1 ⇐⇒ R2 rel_or: R1 ∨ R2 uall: [x:A]. B[x] prop: function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  rel_or: R1 ∨ R2 rel_equivalent: R1 ⇐⇒ R2 infix_ap: y uall: [x:A]. B[x] all: x:A. B[x] iff: ⇐⇒ Q and: P ∧ Q implies:  Q or: P ∨ Q member: t ∈ T prop: rev_implies:  Q
Lemmas referenced :  or_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation independent_pairFormation sqequalHypSubstitution unionElimination thin hypothesis cut lemma_by_obid isectElimination applyEquality hypothesisEquality inlFormation functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    R  \mvee{}  R  \mLeftarrow{}{}\mRightarrow{}  R



Date html generated: 2016_05_14-PM-03_56_15
Last ObjectModification: 2015_12_26-PM-06_55_21

Theory : relations2


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