Nuprl Lemma : poss-maj-length2

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. ∀[x:T]. ∀[n:ℤ].  n ≤ ||L|| supposing (fst(poss-maj(eq;L;x))) = n ∈ ℤ`

Proof

Definitions occuring in Statement :  poss-maj: `poss-maj(eq;L;x)` length: `||as||` list: `T List` deq: `EqDecider(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` pi1: `fst(t)` le: `A ≤ B` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` le: `A ≤ B` and: `P ∧ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` nat: `ℕ`
Lemmas referenced :  deq_wf list_wf nat_wf subtype_rel_product poss-maj_wf pi1_wf equal_wf less_than'_wf int_formula_prop_wf int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformeq_wf itermVar_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt length_wf decidable__le poss-maj-length
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality dependent_functionElimination hypothesis unionElimination equalityTransitivity equalitySymmetry productElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_pairEquality axiomEquality applyEquality setElimination rename lambdaFormation universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:T  List].  \mforall{}[x:T].  \mforall{}[n:\mBbbZ{}].
n  \mleq{}  ||L||  supposing  (fst(poss-maj(eq;L;x)))  =  n

Date html generated: 2016_05_14-PM-03_22_43
Last ObjectModification: 2016_01_14-PM-11_23_15

Theory : decidable!equality

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