Nuprl Lemma : predicate_or_idempotent
∀[T:Type]. ∀[P:T ⟶ ℙ]. P ∨ P ⇐⇒ P
Proof
Definitions occuring in Statement :
predicate_equivalent: P1 ⇐⇒ P2,
predicate_or: P1 ∨ P2,
uall: ∀[x:A]. B[x],
prop: ℙ,
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: 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{}[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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