Nuprl Lemma : append-finite-nat-seq-assoc
∀[f,g,h:finite-nat-seq()]. (f**g**h = f**g**h ∈ finite-nat-seq())
Proof
Definitions occuring in Statement :
append-finite-nat-seq: f**g,
finite-nat-seq: finite-nat-seq(),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
finite-nat-seq: finite-nat-seq(),
append-finite-nat-seq: f**g,
mk-finite-nat-seq: f^(n),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
and: P ∧ Q,
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
less_than: a < b,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
lelt: i ≤ j < k,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
le: A ≤ B,
subtype_rel: A ⊆r B,
subtract: n - m
Lemmas referenced :
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
intformand_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
le_wf,
int_seg_wf,
nat_wf,
finite-nat-seq_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
less_than_wf,
lelt_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
subtract_wf,
int_seg_properties,
itermSubtract_wf,
int_term_value_subtract_lemma,
intformless_wf,
int_formula_prop_less_lemma,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
dependent_pairEquality,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
because_Cache,
independent_pairFormation,
functionEquality,
axiomEquality,
functionExtensionality,
lambdaFormation,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
lessCases,
sqequalAxiom,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
applyEquality,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[f,g,h:finite-nat-seq()]. (f**g**h = f**g**h)
Date html generated:
2017_04_20-AM-07_29_49
Last ObjectModification:
2017_02_27-PM-06_01_03
Theory : continuity
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