### Nuprl Lemma : poss-maj-unanimous

`∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x,y:T.  ((poss-maj(eq;L;x) = <||L||, y> ∈ (ℕ × T)) `` (∀z∈L.z = y ∈ T))`

Proof

Definitions occuring in Statement :  poss-maj: `poss-maj(eq;L;x)` l_all: `(∀x∈L.P[x])` length: `||as||` list: `T List` deq: `EqDecider(T)` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` pair: `<a, b>` product: `x:A × B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` implies: `P `` Q` and: `P ∧ Q` cand: `A c∧ B` uall: `∀[x:A]. B[x]` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` pi1: `fst(t)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` pi2: `snd(t)` l_all: `(∀x∈L.P[x])` sq_type: `SQType(T)` guard: `{T}` deq: `EqDecider(T)` int_seg: `{i..j-}` lelt: `i ≤ j < k` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` eqof: `eqof(d)` bfalse: `ff` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` le: `A ≤ B` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  poss-maj-invariant poss-maj_wf nat_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_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_var_lemma int_formula_prop_wf length_wf_nat and_wf equal_wf pi1_wf le_wf pi2_wf subtype_base_sq set_subtype_base int_subtype_base select_wf int_seg_properties length_wf decidable__lt intformless_wf int_formula_prop_less_lemma bool_wf eqtt_to_assert safe-assert-deq eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot assert_wf eqof_wf not_wf int_seg_wf subtract_wf count_wf bnot_wf all_wf list_wf deq_wf itermSubtract_wf int_term_value_subtract_lemma count-length-filter pos_length filter_wf5 equal-wf-T-base assert_of_null filter_is_empty lelt_wf length-filter
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality cumulativity productEquality productElimination rename sqequalRule isectElimination setElimination natural_numberEquality unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll dependent_set_memberEquality because_Cache equalitySymmetry equalityTransitivity applyLambdaEquality applyEquality promote_hyp instantiate independent_functionElimination hyp_replacement independent_pairEquality equalityElimination addLevel impliesFunctionality levelHypothesis impliesLevelFunctionality functionEquality universeEquality baseClosed

Latex:
\mforall{}T:Type.  \mforall{}eq:EqDecider(T).  \mforall{}L:T  List.  \mforall{}x,y:T.    ((poss-maj(eq;L;x)  =  <||L||,  y>)  {}\mRightarrow{}  (\mforall{}z\mmember{}L.z  =  y))

Date html generated: 2017_04_17-AM-09_08_39
Last ObjectModification: 2017_02_27-PM-05_18_06

Theory : decidable!equality

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