### Nuprl Lemma : member-bag-rep

`∀[T:Type]. ∀[n:ℕ]. ∀[x,y:T].  y = x ∈ T supposing y ↓∈ bag-rep(n;x)`

Proof

Definitions occuring in Statement :  bag-member: `x ↓∈ bs` bag-rep: `bag-rep(n;x)` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  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` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` bag-rep: `bag-rep(n;x)` eq_int: `(i =z j)` subtract: `n - m` ifthenelse: `if b then t else f fi ` btrue: `tt` uiff: `uiff(P;Q)` primrec: `primrec(n;b;c)` empty-bag: `{}` nil: `[]` it: `⋅` decidable: `Dec(P)` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` bfalse: `ff` sq_or: `a ↓∨ b` squash: `↓T` bool: `𝔹` unit: `Unit` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T `
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 bag-member_wf bag-rep_wf list-subtype-bag primrec-unroll bag-member-empty-iff empty-bag_wf nil_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma eq_int_wf bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert assert_of_eq_int eqff_to_assert iff_transitivity assert_wf bnot_wf not_wf equal-wf-base int_subtype_base iff_weakening_uiff assert_of_bnot bag-member-cons primrec_wf bag_wf le_wf cons-bag_wf int_seg_wf equal_wf bool_cases_sqequal assert-bnot neg_assert_of_eq_int nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination axiomEquality cumulativity because_Cache applyEquality equalityTransitivity equalitySymmetry productElimination unionElimination instantiate promote_hyp baseClosed impliesFunctionality dependent_set_memberEquality imageElimination equalityElimination universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[x,y:T].    y  =  x  supposing  y  \mdownarrow{}\mmember{}  bag-rep(n;x)

Date html generated: 2017_10_01-AM-08_54_58
Last ObjectModification: 2017_07_26-PM-04_36_49

Theory : bags

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