Nuprl Lemma : frs-non-dec_wf

[p:ℝ List]. (frs-non-dec(p) ∈ ℙ)


Proof




Definitions occuring in Statement :  frs-non-dec: frs-non-dec(L) real: list: List uall: [x:A]. B[x] prop: member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T frs-non-dec: frs-non-dec(L) so_lambda: λ2x.t[x] implies:  Q prop: int_seg: {i..j-} uimplies: supposing a guard: {T} lelt: i ≤ j < k and: P ∧ Q all: x:A. B[x] decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top less_than: a < b squash: T so_apply: x[s]
Lemmas referenced :  list_wf int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties select_wf rleq_wf le_wf real_wf length_wf int_seg_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis hypothesisEquality lambdaEquality because_Cache functionEquality setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[p:\mBbbR{}  List].  (frs-non-dec(p)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_18-AM-08_51_49
Last ObjectModification: 2016_01_17-AM-02_27_05

Theory : reals


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