### Nuprl Lemma : lifting-2-strict

`∀[f:Top]. ∀[b:bag(Top)].  ((lifting-2(f) {} b ~ {}) ∧ (lifting-2(f) b {} ~ {}))`

Proof

Definitions occuring in Statement :  lifting-2: `lifting-2(f)` empty-bag: `{}` bag: `bag(T)` uall: `∀[x:A]. B[x]` top: `Top` and: `P ∧ Q` apply: `f a` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` and: `P ∧ Q` cand: `A c∧ B` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` lifting-2: `lifting-2(f)` lifting2: `lifting2(f;abag;bbag)` lifting-gen: `lifting-gen(n;f)` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` less_than: `a < b` squash: `↓T` true: `True` empty-bag: `{}` bag-null: `bag-null(bs)` select: `L[n]` cons: `[a / b]` assert: `↑b` ifthenelse: `if b then t else f fi ` btrue: `tt` subtype_rel: `A ⊆r B` subtract: `n - m`
Lemmas referenced :  list_wf bag-subtype-list list-subtype-bag null_wf assert_wf null_nil_lemma lelt_wf int_seg_wf int_term_value_add_lemma int_formula_prop_less_lemma itermAdd_wf intformless_wf decidable__lt length_of_nil_lemma length_of_cons_lemma int_formula_prop_wf 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 itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties nil_wf empty-bag_wf cons_wf top_wf bag_wf select_wf le_wf false_wf lifting-gen-strict
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis hypothesisEquality lambdaEquality because_Cache setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll addEquality independent_pairEquality sqequalAxiom imageMemberEquality baseClosed applyEquality

Latex:
\mforall{}[f:Top].  \mforall{}[b:bag(Top)].    ((lifting-2(f)  \{\}  b  \msim{}  \{\})  \mwedge{}  (lifting-2(f)  b  \{\}  \msim{}  \{\}))

Date html generated: 2016_05_15-PM-03_02_07
Last ObjectModification: 2016_01_16-AM-08_36_35

Theory : bags

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