### Nuprl Lemma : rel_or-restriction

[T:Type]. ∀[P,Q:T ⟶ ℙ]. ∀[R:T ⟶ T ⟶ ℙ].  R|P ∨ R|Q => R|P ∨ Q

Proof

Definitions occuring in Statement :  rel-restriction: R|P predicate_or: P1 ∨ P2 rel_or: R1 ∨ R2 rel_implies: R1 => R2 uall: [x:A]. B[x] prop: function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  predicate_or: P1 ∨ P2 rel-restriction: R|P rel_or: R1 ∨ R2 rel_implies: R1 => R2 infix_ap: y uall: [x:A]. B[x] all: x:A. B[x] implies:  Q and: P ∧ Q cand: c∧ B or: P ∨ Q member: t ∈ T prop:
Lemmas referenced :  or_wf and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut sqequalHypSubstitution unionElimination thin productElimination hypothesis independent_pairFormation inlFormation applyEquality hypothesisEquality inrFormation lemma_by_obid isectElimination functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[P,Q:T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    R|P  \mvee{}  R|Q  =>  R|P  \mvee{}  Q

Date html generated: 2016_05_14-PM-03_56_13
Last ObjectModification: 2015_12_26-PM-06_55_30

Theory : relations2

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