Nuprl Lemma : sublist_antisymmetry
∀[T:Type]. ∀[L1,L2:T List]. (L1 = L2 ∈ (T List)) supposing (L2 ⊆ L1 and L1 ⊆ L2)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top
Lemmas referenced :
proper_sublist_length,
sublist_wf,
list_wf,
length_sublist,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
unionElimination,
productElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. (L1 = L2) supposing (L2 \msubseteq{} L1 and L1 \msubseteq{} L2)
Date html generated:
2018_05_21-PM-00_33_14
Last ObjectModification:
2018_05_19-AM-06_42_52
Theory : list_1
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