### Nuprl Lemma : poss-maj_wf

`∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x:T.  (poss-maj(eq;L;x) ∈ ℕ × T)`

Proof

Definitions occuring in Statement :  poss-maj: `poss-maj(eq;L;x)` list: `T List` deq: `EqDecider(T)` nat: `ℕ` all: `∀x:A. B[x]` member: `t ∈ T` product: `x:A × B[x]` universe: `Type`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` poss-maj: `poss-maj(eq;L;x)` uall: `∀[x:A]. B[x]` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` deq: `EqDecider(T)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` uimplies: `b supposing a` eqof: `eqof(d)` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` int_upper: `{i...}` so_apply: `x[s1;s2]`
Lemmas referenced :  list_accum_wf nat_wf false_wf le_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 eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot eq_int_wf assert_of_eq_int 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 list_wf deq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalRule introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality productEquality hypothesis because_Cache independent_pairEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaEquality productElimination applyEquality setElimination rename unionElimination equalityElimination independent_isectElimination addEquality dependent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll equalityTransitivity equalitySymmetry promote_hyp instantiate independent_functionElimination hypothesis_subsumption universeEquality

Latex:
\mforall{}T:Type.  \mforall{}eq:EqDecider(T).  \mforall{}L:T  List.  \mforall{}x:T.    (poss-maj(eq;L;x)  \mmember{}  \mBbbN{}  \mtimes{}  T)

Date html generated: 2017_04_17-AM-09_08_21
Last ObjectModification: 2017_02_27-PM-05_16_50

Theory : decidable!equality

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