Nuprl Lemma : reg-seq-add_functionality_wrt_bdd-diff
∀x,x',y,y':ℕ+ ⟶ ℤ. (bdd-diff(x;x') ⇒ bdd-diff(y;y') ⇒ bdd-diff(reg-seq-add(x;y);reg-seq-add(x';y')))
Proof
Definitions occuring in Statement :
reg-seq-add: reg-seq-add(x;y),
bdd-diff: bdd-diff(f;g),
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
prop: ℙ,
top: Top,
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
select: L[n],
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
subtract: n - m,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
squash: ↓T,
reg-seq-add: reg-seq-add(x;y),
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat_plus: ℕ+
Lemmas referenced :
reg-seq-list-add_functionality_wrt_bdd-diff,
cons_wf,
nat_plus_wf,
nil_wf,
length_wf,
int_seg_wf,
bdd-diff_wf,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype,
false_wf,
int_seg_cases,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
squash_wf,
true_wf,
equal_wf,
reg-seq-list-add-as-l_sum,
iff_weakening_equal,
map_cons_lemma,
map_nil_lemma,
l_sum_cons_lemma,
l_sum_nil_lemma,
nat_plus_properties,
less_than_wf,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
functionEquality,
hypothesis,
intEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
independent_pairFormation,
natural_numberEquality,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
hypothesis_subsumption,
addEquality,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
computeAll,
hyp_replacement,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality
Latex:
\mforall{}x,x',y,y':\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}.
(bdd-diff(x;x') {}\mRightarrow{} bdd-diff(y;y') {}\mRightarrow{} bdd-diff(reg-seq-add(x;y);reg-seq-add(x';y')))
Date html generated:
2017_10_02-PM-07_14_04
Last ObjectModification:
2017_07_28-AM-07_20_10
Theory : reals
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