Nuprl Lemma : sp-lub_wf
∀[A:ℕ ⟶ Sierpinski]. (lub(n.A[n]) ∈ Sierpinski)
Proof
Definitions occuring in Statement :
sp-lub: lub(n.A[n]),
Sierpinski: Sierpinski,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
Sierpinski: Sierpinski,
subtype_rel: A ⊆r B
Lemmas referenced :
quotient-function-subtype,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
bool_wf,
iff_wf,
equal_wf,
Sierpinski-bottom_wf,
two-class-equiv-rel,
sp-lub_wf1,
Sierpinski_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
functionEquality,
independent_functionElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:\mBbbN{} {}\mrightarrow{} Sierpinski]. (lub(n.A[n]) \mmember{} Sierpinski)
Date html generated:
2019_10_31-AM-06_36_01
Last ObjectModification:
2015_12_28-AM-11_21_20
Theory : synthetic!topology
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