Nuprl Lemma : sublist_transitivity
∀[T:Type]. ∀L1,L2,L3:T List. (L1 ⊆ L2 ⇒ L2 ⊆ L3 ⇒ L1 ⊆ L3)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
sublist: L1 ⊆ L2,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
compose: f o g,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
compose_wf,
int_seg_wf,
length_wf,
increasing_wf,
length_wf_nat,
all_wf,
equal_wf,
select_wf,
int_seg_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,
int_formula_prop_less_lemma,
non_neg_length,
lelt_wf,
nat_properties,
sublist_wf,
list_wf,
compose_increasing
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_pairFormation,
sqequalRule,
productEquality,
cumulativity,
functionExtensionality,
applyEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2,L3:T List. (L1 \msubseteq{} L2 {}\mRightarrow{} L2 \msubseteq{} L3 {}\mRightarrow{} L1 \msubseteq{} L3)
Date html generated:
2018_05_21-PM-00_33_05
Last ObjectModification:
2018_05_19-AM-06_42_47
Theory : list_1
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