Nuprl Lemma : l_contains-append4
∀[T:Type]. ∀A,B,C:T List. (A ⊆ C ⇒ A ⊆ B @ C)
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
or_wf,
uall_wf,
member_append,
list_wf,
all_wf,
int_seg_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
length_wf,
int_seg_properties,
select_wf,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
isect_memberFormation,
lambdaFormation,
hypothesis,
inrFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
universeEquality,
addLevel,
uallFunctionality,
allFunctionality,
impliesFunctionality,
independent_functionElimination,
instantiate,
functionEquality,
introduction,
applyEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B,C:T List. (A \msubseteq{} C {}\mRightarrow{} A \msubseteq{} B @ C)
Date html generated:
2016_05_14-AM-07_55_05
Last ObjectModification:
2016_01_15-AM-08_29_25
Theory : list_1
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