Nuprl Lemma : predicate_or_idempotent

[T:Type]. ∀[P:T ⟶ ℙ].  P ∨ ⇐⇒ P


Proof




Definitions occuring in Statement :  predicate_equivalent: P1 ⇐⇒ P2 predicate_or: P1 ∨ P2 uall: [x:A]. B[x] prop: function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  predicate_or: P1 ∨ P2 predicate_equivalent: P1 ⇐⇒ P2 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{}[P:T  {}\mrightarrow{}  \mBbbP{}].    P  \mvee{}  P  \mLeftarrow{}{}\mRightarrow{}  P



Date html generated: 2016_05_14-AM-06_05_58
Last ObjectModification: 2015_12_26-AM-11_32_29

Theory : relations


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