Nuprl Lemma : last-from-upto
∀[n,m:ℤ]. last([n, m)) ~ m - 1 supposing n < m
Proof
Definitions occuring in Statement :
from-upto: [n, m),
last: last(L),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
last: last(L),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
subtract: n - m
Lemmas referenced :
length-from-upto,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
select-from-upto,
decidable__le,
satisfiable-full-omega-tt,
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,
decidable__lt,
subtract_wf,
lelt_wf,
subtype_base_sq,
int_subtype_base,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
instantiate,
cumulativity,
independent_functionElimination,
promote_hyp,
sqequalAxiom
Latex:
\mforall{}[n,m:\mBbbZ{}]. last([n, m)) \msim{} m - 1 supposing n < m
Date html generated:
2017_04_17-AM-07_55_07
Last ObjectModification:
2017_02_27-PM-04_26_50
Theory : list_1
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