Nuprl Lemma : binrel_ap_wf
∀[T:Type]. ∀[r:T ⟶ T ⟶ ℙ]. ∀[a,b:T]. (a [r] b ∈ ℙ)
Proof
Definitions occuring in Statement :
binrel_ap: a [r] b,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
binrel_ap: a [r] b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[r:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[a,b:T]. (a [r] b \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_00_39
Last ObjectModification:
2015_12_26-PM-11_26_40
Theory : gen_algebra_1
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