### Nuprl Lemma : fan-realizer_test2

`∀m:ℕ. ∃k:ℕ. ∀f:ℕ ⟶ 𝔹. ∃n:ℕk. ((λl.(m ≤ ||l||)) map(f;upto(n)))`

Proof

Definitions occuring in Statement :  upto: `upto(n)` length: `||as||` map: `map(f;as)` int_seg: `{i..j-}` nat: `ℕ` bool: `𝔹` le: `A ≤ B` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` apply: `f a` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  member: `t ∈ T` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` nat: `ℕ` implies: `P `` Q` tbar: `tbar(T;X)` exists: `∃x:A. B[x]` squash: `↓T` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` dec-predicate: `Decidable(X)`
Lemmas referenced :  map_wf int_formula_prop_wf int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma itermVar_wf intformle_wf intformnot_wf satisfiable-full-omega-tt decidable__le nat_properties length_upto iff_weakening_equal upto_wf subtype_rel_self false_wf int_seg_subtype_nat subtype_rel_dep_function int_seg_wf map_length_nat true_wf squash_wf list_wf bool_wf length_wf le_wf nat_wf fan-realizer_wf
Rules used in proof :  cut lemma_by_obid introduction sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity sqequalHypSubstitution equalityTransitivity hypothesis equalitySymmetry lambdaFormation isectElimination thin lambdaEquality setElimination rename hypothesisEquality independent_functionElimination sqequalRule dependent_pairFormation applyEquality imageElimination intEquality natural_numberEquality independent_isectElimination independent_pairFormation because_Cache imageMemberEquality baseClosed universeEquality productElimination dependent_functionElimination unionElimination int_eqEquality isect_memberEquality voidElimination voidEquality computeAll functionEquality

Latex:
\mforall{}m:\mBbbN{}.  \mexists{}k:\mBbbN{}.  \mforall{}f:\mBbbN{}  {}\mrightarrow{}  \mBbbB{}.  \mexists{}n:\mBbbN{}k.  ((\mlambda{}l.(m  \mleq{}  ||l||))  map(f;upto(n)))

Date html generated: 2016_05_15-PM-10_05_29
Last ObjectModification: 2016_01_16-PM-04_05_33

Theory : bar!induction

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