### Nuprl Lemma : strong-continuity-test-bound_wf

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

Proof

Definitions occuring in Statement :  strong-continuity-test-bound: `strong-continuity-test-bound(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` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` decidable: `Dec(P)` or: `P ∨ Q` strong-continuity-test-bound: `strong-continuity-test-bound(M;n;f;b)` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` exposed-it: `exposed-it` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` le: `A ≤ B` less_than': `less_than'(a;b)`
Lemmas referenced :  int_seg_wf nat_wf unit_wf2 nat_properties satisfiable-full-omega-tt 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 primrec-unroll-1 lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot eq_int_wf assert_of_eq_int neg_assert_of_eq_int isl_wf le_wf subtype_rel_dep_function int_seg_subtype false_wf primrec_wf int_seg_subtype_nat
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality hypothesis because_Cache functionEquality cumulativity unionEquality universeEquality isect_memberFormation sqequalRule axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality intWeakElimination lambdaFormation independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination unionElimination inrEquality productElimination dependent_set_memberEquality equalityElimination promote_hyp instantiate inlEquality applyEquality functionExtensionality

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

Date html generated: 2017_04_17-AM-10_00_35
Last ObjectModification: 2017_02_27-PM-05_53_04

Theory : continuity

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