Nuprl Lemma : iseg_same_length
∀[T:Type]. ∀[L1,L2:T List]. (L1 = L2 ∈ (T List)) supposing ((||L1|| = ||L2|| ∈ ℤ) and L1 ≤ L2)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A
Lemmas referenced :
list-cases,
product_subtype_list,
equal_wf,
length_wf,
iseg_wf,
list_wf,
append-nil,
subtype_rel_list,
top_wf,
length_wf_nat,
nat_wf,
length-append,
length_of_cons_lemma,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
sqequalRule,
intEquality,
cumulativity,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
hyp_replacement,
Error :applyLambdaEquality,
setElimination,
rename,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. (L1 = L2) supposing ((||L1|| = ||L2||) and L1 \mleq{} L2)
Date html generated:
2016_10_21-AM-10_08_22
Last ObjectModification:
2016_07_12-AM-05_27_48
Theory : list_1
Home
Index