Nuprl Lemma : iseg_select2
∀[T:Type]. ∀[l1,l2:T List]. {∀[i:ℕ||l1||]. (l1[i] = l2[i] ∈ T)} supposing l1 ≤ l2
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
iseg_wf,
int_seg_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
int_seg_properties,
false_wf,
length_wf,
int_seg_subtype_nat,
iseg_select
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
hypothesis,
applyEquality,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. \{\mforall{}[i:\mBbbN{}||l1||]. (l1[i] = l2[i])\} supposing l1 \mleq{} l2
Date html generated:
2016_05_14-PM-01_34_28
Last ObjectModification:
2016_01_15-AM-08_26_00
Theory : list_1
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