Nuprl Lemma : iseg_append_length
∀[T:Type]. ∀l1,l2,l3:T List. (l1 ≤ l2 @ l3 ⇒ l1 ≤ l2 supposing ||l1|| ≤ ||l2||)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
length: ||as||,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
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,
uimplies: b supposing a,
member: t ∈ T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ,
iff: P ⇐⇒ Q,
or: P ∨ Q,
exists: ∃x:A. B[x],
squash: ↓T,
subtype_rel: A ⊆r B,
top: Top,
true: True,
guard: {T},
less_than: a < b,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Lemmas referenced :
less_than'_wf,
length_wf,
iseg_append_iff,
equal_wf,
squash_wf,
true_wf,
length_append,
subtype_rel_list,
top_wf,
iff_weakening_equal,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
intformless_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
le_wf,
iseg_wf,
append_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
rename,
independent_functionElimination,
unionElimination,
applyLambdaEquality,
applyEquality,
imageElimination,
because_Cache,
intEquality,
independent_isectElimination,
isect_memberEquality,
voidEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2,l3:T List. (l1 \mleq{} l2 @ l3 {}\mRightarrow{} l1 \mleq{} l2 supposing ||l1|| \mleq{} ||l2||)
Date html generated:
2017_04_17-AM-08_46_35
Last ObjectModification:
2017_02_27-PM-05_03_42
Theory : list_1
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