Nuprl Lemma : greatest-lower-bound_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[a,b,c:T]. (greatest-lower-bound(T;x,y.R[x;y];a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
greatest-lower-bound: greatest-lower-bound(T;x,y.R[x; y];a;b;c),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
greatest-lower-bound: greatest-lower-bound(T;x,y.R[x; y];a;b;c),
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
and_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[a,b,c:T]. (greatest-lower-bound(T;x,y.R[x;y];a;b;c) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-04_18_25
Last ObjectModification:
2015_12_26-AM-11_27_43
Theory : rel_1
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