Nuprl Lemma : from-upto-is-singleton
∀[n,m:ℤ]. [n, m) = [n] ∈ (ℤ List) supposing m = (n + 1) ∈ ℤ
Proof
Definitions occuring in Statement :
from-upto: [n, m),
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
from-upto: [n, m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
has-value: (a)↓,
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,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
value-type-has-value,
int-value-type,
from-upto-nil,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
cons_wf,
nil_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
less_than_wf,
intformless_wf,
int_formula_prop_less_lemma,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalRule,
addEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
callbyvalueReduce,
because_Cache,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
promote_hyp,
applyEquality,
baseApply,
closedConclusion,
baseClosed,
axiomEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. [n, m) = [n] supposing m = (n + 1)
Date html generated:
2017_04_17-AM-07_56_15
Last ObjectModification:
2017_02_27-PM-04_28_03
Theory : list_1
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