Nuprl Lemma : not-isl-priority-select

[T:Type]. ∀[as:T List]. ∀[f,g:T ⟶ 𝔹].  uiff(¬↑isl(priority-select(f;g;as));(∀a∈as.(¬↑(f a)) ∧ (¬↑(g a))))


Proof




Definitions occuring in Statement :  priority-select: priority-select(f;g;as) l_all: (∀x∈L.P[x]) list: List assert: b isl: isl(x) bool: 𝔹 uiff: uiff(P;Q) uall: [x:A]. B[x] not: ¬A and: P ∧ Q apply: a function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  member: t ∈ T uall: [x:A]. B[x] all: x:A. B[x] implies:  Q uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a prop: not: ¬A false: False isl: isl(x) rev_implies:  Q so_lambda: λ2x.t[x] so_apply: x[s] iff: ⇐⇒ Q l_all: (∀x∈L.P[x]) int_seg: {i..j-} guard: {T} lelt: i ≤ j < k decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top less_than: a < b squash: T subtype_rel: A ⊆B assert: b ifthenelse: if then else fi  btrue: tt true: True bfalse: ff
Lemmas referenced :  priority-select_wf bool_wf unit_wf2 not_wf assert_wf isl_wf assert_elim and_wf equal_wf bfalse_wf btrue_neq_bfalse equal-wf-T-base iff_weakening_uiff l_all_wf2 l_member_wf priority-select-inr select_wf int_seg_properties length_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma int_seg_wf uiff_wf list_wf equal-unit it_wf
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality functionExtensionality applyEquality hypothesis unionEquality lambdaFormation independent_pairFormation isect_memberFormation addLevel independent_isectElimination levelHypothesis dependent_set_memberEquality equalityTransitivity equalitySymmetry applyLambdaEquality setElimination rename productElimination sqequalRule independent_functionElimination voidElimination lambdaEquality dependent_functionElimination because_Cache productEquality setEquality baseClosed independent_pairEquality natural_numberEquality unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidEquality computeAll imageElimination universeEquality functionEquality inrEquality

Latex:
\mforall{}[T:Type].  \mforall{}[as:T  List].  \mforall{}[f,g:T  {}\mrightarrow{}  \mBbbB{}].
    uiff(\mneg{}\muparrow{}isl(priority-select(f;g;as));(\mforall{}a\mmember{}as.(\mneg{}\muparrow{}(f  a))  \mwedge{}  (\mneg{}\muparrow{}(g  a))))



Date html generated: 2018_05_21-PM-06_49_50
Last ObjectModification: 2017_07_26-PM-04_56_55

Theory : general


Home Index