### Nuprl Lemma : strong-continuity-test_wf

`∀[T:Type]. ∀[M:n:ℕ ⟶ (ℕn ⟶ T) ⟶ (ℕ?)]. ∀[n:ℕ]. ∀[f:ℕn ⟶ T]. ∀[b:ℕ?].  (strong-continuity-test(M;n;f;b) ∈ ℕ?)`

Proof

Definitions occuring in Statement :  strong-continuity-test: `strong-continuity-test(M;n;f;b)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` unit: `Unit` member: `t ∈ T` function: `x:A ⟶ B[x]` union: `left + right` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  member: `t ∈ T` uall: `∀[x:A]. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` decidable: `Dec(P)` or: `P ∨ Q` strong-continuity-test: `strong-continuity-test(M;n;f;b)` lelt: `i ≤ j < k` int_seg: `{i..j-}` assert: `↑b` bnot: `¬bb` guard: `{T}` sq_type: `SQType(T)` bfalse: `ff` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` btrue: `tt` it: `⋅` unit: `Unit` bool: `𝔹` exposed-it: `exposed-it` less_than': `less_than'(a;b)` le: `A ≤ B` so_apply: `x[s]` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B`
Lemmas referenced :  nat_wf unit_wf2 int_seg_wf nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma primrec0_lemma int_seg_properties int_seg_subtype_nat primrec_wf assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert eqtt_to_assert bool_wf false_wf int_seg_subtype subtype_rel_dep_function le_wf satisfiable-full-omega-tt isl_wf primrec-unroll-1
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity unionEquality cut introduction extract_by_obid hypothesis because_Cache functionEquality sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality universeEquality isect_memberFormation sqequalRule axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality intWeakElimination lambdaFormation independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination voidElimination voidEquality independent_pairFormation unionElimination cumulativity instantiate promote_hyp inrEquality productElimination equalityElimination computeAll functionExtensionality applyEquality dependent_set_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[M:n:\mBbbN{}  {}\mrightarrow{}  (\mBbbN{}n  {}\mrightarrow{}  T)  {}\mrightarrow{}  (\mBbbN{}?)].  \mforall{}[n:\mBbbN{}].  \mforall{}[f:\mBbbN{}n  {}\mrightarrow{}  T].  \mforall{}[b:\mBbbN{}?].
(strong-continuity-test(M;n;f;b)  \mmember{}  \mBbbN{}?)

Date html generated: 2019_06_20-PM-02_49_59
Last ObjectModification: 2018_09_26-AM-09_54_20

Theory : continuity

Home Index