Nuprl Lemma : lower-bound_wf

[A:Set(ℝ)]. ∀[b:ℝ].  (lower-bound(A;b) ∈ ℙ)


Proof




Definitions occuring in Statement :  lower-bound: lower-bound(A;b) rset: Set(ℝ) real: uall: [x:A]. B[x] prop: member: t ∈ T
Definitions unfolded in proof :  lower-bound: lower-bound(A;b) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] implies:  Q prop: so_apply: x[s]
Lemmas referenced :  all_wf real_wf rset-member_wf rleq_wf rset_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality functionEquality hypothesisEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[A:Set(\mBbbR{})].  \mforall{}[b:\mBbbR{}].    (lower-bound(A;b)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_18-AM-08_09_31
Last ObjectModification: 2015_12_28-AM-01_15_49

Theory : reals


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