### Nuprl Lemma : strong-continuity2-weak-skolem

`∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ].  (strong-continuity2(T;F) `` weak-continuity-skolem(T;F))`

Proof

Definitions occuring in Statement :  weak-continuity-skolem: `weak-continuity-skolem(T;F)` strong-continuity2: `strong-continuity2(T;F)` nat: `ℕ` uall: `∀[x:A]. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` implies: `P `` Q` strong-continuity2: `strong-continuity2(T;F)` exists: `∃x:A. B[x]` weak-continuity-skolem: `weak-continuity-skolem(T;F)` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` so_apply: `x[s]` nat: `ℕ` uimplies: `b supposing a` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` all: `∀x:A. B[x]` pi1: `fst(t)` isl: `isl(x)` sq_type: `SQType(T)` guard: `{T}` assert: `↑b` ifthenelse: `if b then t else f fi ` btrue: `tt` true: `True` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  strong-continuity2_wf nat_wf exists_wf equal_wf subtype_rel_dep_function int_seg_wf int_seg_subtype_nat false_wf all_wf isect_wf assert_wf isl_wf unit_wf2 and_wf btrue_wf subtype_base_sq bool_wf bool_subtype_base nat_properties 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__equal_int intformeq_wf int_formula_prop_eq_lemma le_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin cut introduction extract_by_obid isectElimination cumulativity hypothesisEquality functionExtensionality applyEquality functionEquality hypothesis universeEquality rename dependent_pairFormation lambdaEquality because_Cache productEquality sqequalRule natural_numberEquality setElimination independent_isectElimination independent_pairFormation inlEquality unionEquality independent_pairEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination dependent_set_memberEquality applyLambdaEquality instantiate unionElimination int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll promote_hyp

Latex:
\mforall{}[T:Type].  \mforall{}[F:(\mBbbN{}  {}\mrightarrow{}  T)  {}\mrightarrow{}  \mBbbN{}].    (strong-continuity2(T;F)  {}\mRightarrow{}  weak-continuity-skolem(T;F))

Date html generated: 2017_04_17-AM-09_54_03
Last ObjectModification: 2017_02_27-PM-05_49_09

Theory : continuity

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