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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