### Nuprl Lemma : baf-bar_wf

`∀[R,T:ℕ ⟶ ℕ ⟶ ℙ]. ∀[l:ℕ]. ∀[a:x:ℕl ⟶ ℕ].  (baf-bar(n,m.R[n;m];n,m.T[n;m];l;a) ∈ ℙ)`

Proof

Definitions occuring in Statement :  baf-bar: `baf-bar(n,m.R[n; m];n,m.T[n; m];l;a)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` baf-bar: `baf-bar(n,m.R[n; m];n,m.T[n; m];l;a)` prop: `ℙ` and: `P ∧ Q` subtype_rel: `A ⊆r B` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` all: `∀x:A. B[x]` int_seg: `{i..j-}` so_apply: `x[s1;s2]` lelt: `i ≤ j < k` guard: `{T}` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top`
Lemmas referenced :  lelt_wf int_formula_prop_wf int_term_value_add_lemma 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 itermAdd_wf itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties int_seg_properties exists_wf nat_wf int_seg_wf subtype_rel_dep_function strictly-increasing-seq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality applyEquality natural_numberEquality setElimination rename hypothesis lambdaEquality because_Cache intEquality independent_isectElimination lambdaFormation addEquality dependent_set_memberEquality productElimination independent_pairFormation dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll universeEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity

Latex:
\mforall{}[R,T:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[l:\mBbbN{}].  \mforall{}[a:x:\mBbbN{}l  {}\mrightarrow{}  \mBbbN{}].    (baf-bar(n,m.R[n;m];n,m.T[n;m];l;a)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-PM-09_51_26
Last ObjectModification: 2016_01_15-PM-10_54_20

Theory : continuity

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