Nuprl Lemma : from-upto-single
∀[n:ℤ]. ([n, n + 1) ~ [n])
Proof
Definitions occuring in Statement :
from-upto: [n, m),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
label: ...$L... t,
cand: A c∧ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T)
Lemmas referenced :
subtype_base_sq,
list_wf,
le_wf,
less_than_wf,
list_subtype_base,
set_subtype_base,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
from-upto-is-singleton,
strong-subtype-equal-lists,
strong-subtype-set3,
strong-subtype-self,
from-upto_wf,
cons_wf,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
nil_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
setEquality,
intEquality,
productEquality,
hypothesisEquality,
hypothesis,
addEquality,
natural_numberEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_pairFormation,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[n:\mBbbZ{}]. ([n, n + 1) \msim{} [n])
Date html generated:
2017_04_17-AM-07_56_26
Last ObjectModification:
2017_02_27-PM-04_27_55
Theory : list_1
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