Nuprl Lemma : pair_wf_l_member
∀[T:Type]. ∀[L:T List]. ∀[x:T]. ∀[i:ℕ||L||]. <i, Ax, Ax> ∈ (x ∈ L) supposing L[i] = x ∈ T
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
pair: <a, b>,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
cand: A c∧ B,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
int_seg_subtype_nat,
length_wf,
false_wf,
member-less_than,
int_seg_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
less_than_wf,
equal_wf,
select_wf,
nat_properties,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_pairEquality,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesis,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
independent_pairEquality,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalitySymmetry,
productEquality,
because_Cache,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[x:T]. \mforall{}[i:\mBbbN{}||L||]. <i, Ax, Ax> \mmember{} (x \mmember{} L) supposing L[i] = x
Date html generated:
2017_10_01-AM-09_15_34
Last ObjectModification:
2017_07_26-PM-04_50_17
Theory : general
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