Nuprl Lemma : int-list-member-append
∀[i:ℤ]. ∀[xs,ys:ℤ List]. (int-list-member(i;xs @ ys) ~ int-list-member(i;xs) ∨bint-list-member(i;ys))
Proof
Definitions occuring in Statement :
int-list-member: int-list-member(i;xs),
append: as @ bs,
list: T List,
bor: p ∨bq,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
int-list-member: int-list-member(i;xs),
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b)
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
equal-wf-base,
nat_wf,
list_subtype_base,
int_subtype_base,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
list_ind_nil_lemma,
reduce_nil_lemma,
product_subtype_list,
spread_cons_lemma,
colength_wf_list,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
equal-wf-T-base,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
decidable__equal_int,
list_ind_cons_lemma,
reduce_cons_lemma,
bool_wf,
bool_subtype_base,
bor_assoc,
bor_wf,
eq_int_wf,
int-list-member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
instantiate,
cumulativity,
imageElimination
Latex:
\mforall{}[i:\mBbbZ{}]. \mforall{}[xs,ys:\mBbbZ{} List].
(int-list-member(i;xs @ ys) \msim{} int-list-member(i;xs) \mvee{}\msubb{}int-list-member(i;ys))
Date html generated:
2018_05_21-PM-07_31_56
Last ObjectModification:
2017_07_26-PM-05_07_08
Theory : general
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