### Nuprl Lemma : lifting-gen-strict

`∀[n:ℕ]. ∀[f:Top]. ∀[a:k:ℕn ⟶ bag(Top)].  lifting-gen(n;f) a ~ {} supposing ∃k:ℕn. (↑bag-null(a k))`

Proof

Definitions occuring in Statement :  lifting-gen: `lifting-gen(n;f)` bag-null: `bag-null(bs)` empty-bag: `{}` bag: `bag(T)` int_seg: `{i..j-}` nat: `ℕ` assert: `↑b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` top: `Top` exists: `∃x:A. B[x]` apply: `f a` function: `x:A ⟶ B[x]` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  lifting-gen: `lifting-gen(n;f)` lifting-gen-rev: `lifting-gen-rev(n;f;bags)` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` 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` top: `Top` and: `P ∧ Q` prop: `ℙ` so_lambda: `λ2x.t[x]` le: `A ≤ B` int_seg: `{i..j-}` lelt: `i ≤ j < k` so_apply: `x[s]` guard: `{T}` decidable: `Dec(P)` or: `P ∨ Q` lifting-gen-list-rev: `lifting-gen-list-rev(n;bags)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` less_than': `less_than'(a;b)`
Lemmas referenced :  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 exists_wf int_seg_wf assert_wf bag-null_wf top_wf itermSubtract_wf int_term_value_subtract_lemma lelt_wf bag_wf le_wf subtract_wf nat_wf int_seg_properties decidable__le intformnot_wf int_formula_prop_not_lemma eq_int_wf bool_wf uiff_transitivity equal-wf-T-base equal_wf eqtt_to_assert assert_of_eq_int intformeq_wf int_formula_prop_eq_lemma iff_transitivity bnot_wf not_wf iff_weakening_uiff eqff_to_assert assert_of_bnot itermAdd_wf int_term_value_add_lemma decidable__equal_int bag-combine-empty-left bag-combine-empty-right decidable__lt false_wf assert-bag-null equal-empty-bag
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep cut lambdaFormation introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination sqequalAxiom because_Cache applyEquality functionExtensionality productElimination dependent_set_memberEquality equalityTransitivity equalitySymmetry functionEquality isect_memberFormation unionElimination equalityElimination baseClosed impliesFunctionality addEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f:Top].  \mforall{}[a:k:\mBbbN{}n  {}\mrightarrow{}  bag(Top)].    lifting-gen(n;f)  a  \msim{}  \{\}  supposing  \mexists{}k:\mBbbN{}n.  (\muparrow{}bag-null(a  k))

Date html generated: 2017_10_01-AM-09_03_01
Last ObjectModification: 2017_07_26-PM-04_44_01

Theory : bags

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