Nuprl Lemma : sublist_append_front
∀[T:Type]. ∀L,L1,L2:T List. L ⊆ L1 @ L2 ⇒ L ⊆ L1 supposing ¬(last(L) ∈ L2) supposing ¬↑null(L)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
last: last(L),
l_member: (x ∈ l),
null: null(as),
append: as @ bs,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
top: Top,
sublist: L1 ⊆ L2,
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
subtype_rel: A ⊆r B,
l_member: (x ∈ l),
nat: ℕ,
cand: A c∧ B,
ge: i ≥ j ,
le: A ≤ B,
last: last(L),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member_wf,
last_wf,
not_wf,
assert_wf,
null_wf,
decidable__assert,
sublist_wf,
append_wf,
isect_wf,
list_wf,
assert_of_null,
nil-sublist,
non_nil_length,
not_functionality_wrt_uiff,
equal-wf-T-base,
decidable__lt,
int_seg_wf,
length_wf,
subtract_wf,
length-append,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
lelt_wf,
le_wf,
non_neg_length,
length_append,
subtype_rel_list,
top_wf,
length_wf_nat,
nat_properties,
int_seg_properties,
itermAdd_wf,
int_term_value_add_lemma,
less_than_wf,
equal_wf,
select_wf,
squash_wf,
true_wf,
select_append_back,
subtype_rel_self,
iff_weakening_equal,
add-is-int-iff,
false_wf,
increasing_implies_le,
nat_wf,
select_append_front,
increasing_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
voidElimination,
extract_by_obid,
independent_isectElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
rename,
unionElimination,
universeEquality,
productElimination,
voidEquality,
hyp_replacement,
applyLambdaEquality,
because_Cache,
baseClosed,
independent_functionElimination,
applyEquality,
functionExtensionality,
natural_numberEquality,
cumulativity,
dependent_set_memberEquality,
independent_pairFormation,
imageElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
setElimination,
productEquality,
imageMemberEquality,
instantiate,
addEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion
Latex:
\mforall{}[T:Type]. \mforall{}L,L1,L2:T List. L \msubseteq{} L1 @ L2 {}\mRightarrow{} L \msubseteq{} L1 supposing \mneg{}(last(L) \mmember{} L2) supposing \mneg{}\muparrow{}null(L)
Date html generated:
2019_06_20-PM-01_22_51
Last ObjectModification:
2018_09_17-PM-06_04_14
Theory : list_1
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