Nuprl Lemma : rel_or_idempotent
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. R ∨ R ⇐⇒ R
Proof
Definitions occuring in Statement :
rel_equivalent: R1 ⇐⇒ R2,
rel_or: R1 ∨ R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_or: R1 ∨ R2,
rel_equivalent: R1 ⇐⇒ R2,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ 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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