Nuprl Lemma : strict-upper-bounds_wf

[A:Set(ℝ)]. (strict-upper-bounds(A) ∈ Set(ℝ))


Proof




Definitions occuring in Statement :  strict-upper-bounds: strict-upper-bounds(A) rset: Set(ℝ) uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  strict-upper-bounds: strict-upper-bounds(A) rset: Set(ℝ) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] implies:  Q prop: so_apply: x[s] all: x:A. B[x] strict-upper-bound: A < b guard: {T} uimplies: supposing a
Lemmas referenced :  strict-upper-bound_wf all_wf real_wf req_wf rless_transitivity1 rleq_weakening rset-member_wf set_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut setElimination thin rename dependent_set_memberEquality lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination hypothesis hypothesisEquality functionEquality applyEquality because_Cache lambdaFormation dependent_functionElimination independent_functionElimination independent_isectElimination axiomEquality equalityTransitivity equalitySymmetry instantiate cumulativity universeEquality

Latex:
\mforall{}[A:Set(\mBbbR{})].  (strict-upper-bounds(A)  \mmember{}  Set(\mBbbR{}))



Date html generated: 2016_05_18-AM-08_11_49
Last ObjectModification: 2015_12_28-AM-01_17_08

Theory : reals


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