Nuprl Lemma : lifting-0_wf

`∀[B:Type]. ∀[b:B].  (lifting-0(b) ∈ bag(B))`

Proof

Definitions occuring in Statement :  lifting-0: `lifting-0(b)` bag: `bag(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` lifting-0: `lifting-0(b)` select: `L[n]` uimplies: `b supposing a` all: `∀x:A. B[x]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` top: `Top` so_apply: `x[s1;s2]` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` funtype: `funtype(n;A;T)` primrec: `primrec(n;b;c)` lifting-gen-rev: `lifting-gen-rev(n;f;bags)` lifting-gen-list-rev: `lifting-gen-list-rev(n;bags)` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` btrue: `tt` single-bag: `{x}` cons: `[a / b]`
Lemmas referenced :  subtype_rel_self int_seg_wf int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermVar_wf intformless_wf intformand_wf satisfiable-full-omega-tt int_seg_properties le_wf false_wf lifting-gen-rev_wf base_wf stuck-spread
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed independent_isectElimination lambdaFormation hypothesis isect_memberEquality voidElimination voidEquality because_Cache dependent_set_memberEquality natural_numberEquality independent_pairFormation hypothesisEquality lambdaEquality setElimination rename productElimination dependent_pairFormation int_eqEquality intEquality dependent_functionElimination computeAll applyEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[B:Type].  \mforall{}[b:B].    (lifting-0(b)  \mmember{}  bag(B))

Date html generated: 2016_05_15-PM-03_01_15
Last ObjectModification: 2016_01_16-AM-08_36_27

Theory : bags

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