Nuprl Lemma : proper-iseg-append-one
∀[T:Type]. ∀L1,L2:T List. ∀x:T. (L1 < L2 @ [x] ⇐⇒ L1 ≤ L2)
Proof
Definitions occuring in Statement :
proper-iseg: L1 < L2,
iseg: l1 ≤ l2,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
proper-iseg: L1 < L2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
or: P ∨ Q,
exists: ∃x:A. B[x],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
cons: [a / b],
top: Top,
bfalse: ff,
uimplies: b supposing a,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Lemmas referenced :
iseg_wf,
append_wf,
cons_wf,
nil_wf,
not_wf,
equal_wf,
list_wf,
iseg_append,
iseg_append_iff,
iseg_single,
and_wf,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
iseg_length,
length-append,
satisfiable-full-omega-tt,
intformle_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
productEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
universeEquality,
unionElimination,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
imageElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
hyp_replacement,
Error :applyLambdaEquality,
independent_isectElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. \mforall{}x:T. (L1 < L2 @ [x] \mLeftarrow{}{}\mRightarrow{} L1 \mleq{} L2)
Date html generated:
2016_10_21-AM-10_32_43
Last ObjectModification:
2016_07_12-AM-05_45_34
Theory : list_1
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