Nuprl Lemma : ibs-property
∀[s:IBS]. ∀[m:ℕ]. ∀[n:ℕ]. (s n) = 1 ∈ ℤ supposing m ≤ n supposing (s m) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
incr-binary-seq: IBS,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
apply: f a,
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,
incr-binary-seq: IBS,
so_lambda: λ2x.t[x],
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
so_apply: x[s],
sq_stable: SqStable(P),
sq_type: SQType(T),
guard: {T},
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
subtract: n - m
Lemmas referenced :
sq_stable__all,
nat_wf,
equal-wf-base,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
set_subtype_base,
lelt_wf,
int_subtype_base,
sq_stable__equal,
int_seg_wf,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
istype-less_than,
add-zero,
subtract-1-ge-0,
subtype_base_sq,
decidable__equal_int,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
subtract_wf,
le_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
int_seg_properties,
istype-nat,
incr-binary-seq_wf,
minus-one-mul,
add-commutes,
add-associates,
add-mul-special,
zero-mul,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality_alt,
intEquality,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality_alt,
addEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
baseClosed,
lambdaFormation_alt,
axiomEquality,
functionIsTypeImplies,
intWeakElimination,
instantiate,
cumulativity,
imageElimination,
imageMemberEquality,
universeEquality,
productElimination,
applyLambdaEquality,
equalityIstype,
isectIsTypeImplies,
sqequalBase
Latex:
\mforall{}[s:IBS]. \mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}]. (s n) = 1 supposing m \mleq{} n supposing (s m) = 1
Date html generated:
2019_10_30-AM-10_15_43
Last ObjectModification:
2019_06_28-PM-01_55_36
Theory : real!vectors
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