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: ℙ,
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: x f y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ
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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