Nuprl Lemma : rel_plus-of-restriction
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[P:T ⟶ ℙ]. R|P+ => R+|P
Proof
Definitions occuring in Statement :
rel_plus: R+,
rel-restriction: R|P,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
rel-restriction: R|P,
rel_implies: R1 => R2,
infix_ap: x f y,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
rel_plus_minimal,
rel-restriction_wf,
rel_plus_wf,
and_wf,
rel-rel-plus,
restriction-of-transitive,
rel_plus_trans
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
independent_functionElimination,
lambdaFormation,
productElimination,
independent_pairFormation,
applyEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. R|P\msupplus{} => R\msupplus{}|P
Date html generated:
2016_05_14-PM-03_55_32
Last ObjectModification:
2015_12_26-PM-06_55_38
Theory : relations2
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