Nuprl Lemma : proper_sublist_length
∀[T:Type]. ∀[L1,L2:T List]. (L1 = L2 ∈ (T List)) supposing ((||L1|| = ||L2|| ∈ ℤ) and L1 ⊆ L2)
Proof
Definitions occuring in Statement :
sublist: 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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
sublist: L1 ⊆ L2,
exists: ∃x:A. B[x],
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
guard: {T},
squash: ↓T,
cand: A c∧ B,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_extensionality,
less_than_wf,
length_wf,
nat_wf,
equal_wf,
sublist_wf,
list_wf,
lelt_wf,
increasing_is_id,
length_wf_nat,
int_seg_subtype,
false_wf,
le_weakening,
int_seg_wf,
squash_wf,
true_wf,
select_wf,
le_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
lambdaFormation,
setElimination,
rename,
Error :universeIsType,
intEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
Error :inhabitedIsType,
universeEquality,
productElimination,
dependent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
natural_numberEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
imageElimination,
productEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
imageMemberEquality,
baseClosed,
instantiate
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. (L1 = L2) supposing ((||L1|| = ||L2||) and L1 \msubseteq{} L2)
Date html generated:
2019_06_20-PM-01_22_24
Last ObjectModification:
2018_09_26-PM-05_20_51
Theory : list_1
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