### Nuprl Lemma : poss-maj-member

`∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x:T.  (snd(poss-maj(eq;L;x)) ∈ [x / L])`

Proof

Definitions occuring in Statement :  poss-maj: `poss-maj(eq;L;x)` l_member: `(x ∈ l)` cons: `[a / b]` list: `T List` deq: `EqDecider(T)` pi2: `snd(t)` all: `∀x:A. B[x]` universe: `Type`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` poss-maj: `poss-maj(eq;L;x)` so_lambda: `λ2x.t[x]` so_lambda: `λ2x y.t[x; y]` deq: `EqDecider(T)` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` eqof: `eqof(d)` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` le: `A ≤ B` less_than': `less_than'(a;b)` int_upper: `{i...}` so_apply: `x[s1;s2]` so_apply: `x[s]` pi2: `snd(t)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` gt: `i > j`
Lemmas referenced :  list_wf deq_wf list_induction all_wf nat_wf l_member_wf list_accum_wf bool_wf eqtt_to_assert safe-assert-deq nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf le_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot eq_int_wf assert_of_eq_int false_wf neg_assert_of_eq_int int_upper_subtype_nat nequal-le-implies zero-add subtract_wf int_upper_properties itermSubtract_wf int_term_value_subtract_lemma pi2_wf cons_wf list_accum_nil_lemma cons_member nil_wf list_accum_cons_lemma equal-wf-T-base assert_wf bnot_wf not_wf eqof_wf uiff_transitivity iff_transitivity iff_weakening_uiff assert_of_bnot ifthenelse_wf decidable__lt intformless_wf intformeq_wf int_formula_prop_less_lemma int_formula_prop_eq_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation hypothesisEquality cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesis universeEquality sqequalRule lambdaEquality because_Cache productElimination applyEquality setElimination rename unionElimination equalityElimination independent_isectElimination independent_pairEquality dependent_set_memberEquality addEquality natural_numberEquality dependent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll equalityTransitivity equalitySymmetry promote_hyp instantiate independent_functionElimination hypothesis_subsumption productEquality inlFormation baseClosed addLevel impliesFunctionality levelHypothesis spreadEquality inrFormation hyp_replacement applyLambdaEquality

Latex:
\mforall{}T:Type.  \mforall{}eq:EqDecider(T).  \mforall{}L:T  List.  \mforall{}x:T.    (snd(poss-maj(eq;L;x))  \mmember{}  [x  /  L])

Date html generated: 2017_04_17-AM-09_08_45
Last ObjectModification: 2017_02_27-PM-05_17_35

Theory : decidable!equality

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