Nuprl Lemma : make-strict-agrees
∀[alpha:ℕ ⟶ ℕ]. ∀[n:ℕ]. ∀[i:ℕn]. ((make-strict(alpha) i) = (alpha i) ∈ ℤ) supposing strictly-increasing-seq(n;alpha)
Proof
Definitions occuring in Statement :
make-strict: make-strict(alpha),
strictly-increasing-seq: strictly-increasing-seq(n;s),
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
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,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
strictly-increasing-seq: strictly-increasing-seq(n;s),
make-strict: make-strict(alpha),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
strict-inc: StrictInc,
squash: ↓T,
true: True
Lemmas referenced :
int_seg_wf,
strictly-increasing-seq_wf,
subtype_rel_dep_function,
nat_wf,
int_seg_subtype_nat,
istype-false,
istype-nat,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
int_seg_properties,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
istype-le,
subtract-1-ge-0,
decidable__lt,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtract_wf,
primrec-unroll,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
subtract-add-cancel,
make-strict_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
sqequalHypSubstitution,
independent_functionElimination,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
Error :universeIsType,
extract_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
sqequalRule,
Error :isect_memberEquality_alt,
axiomEquality,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
applyEquality,
Error :lambdaEquality_alt,
intEquality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
Error :lambdaFormation_alt,
Error :functionIsType,
intWeakElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
voidElimination,
Error :functionIsTypeImplies,
productElimination,
Error :dependent_set_memberEquality_alt,
unionElimination,
Error :productIsType,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
Error :equalityIstype,
promote_hyp,
instantiate,
cumulativity,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[alpha:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n:\mBbbN{}].
\mforall{}[i:\mBbbN{}n]. ((make-strict(alpha) i) = (alpha i)) supposing strictly-increasing-seq(n;alpha)
Date html generated:
2019_06_20-PM-02_57_20
Last ObjectModification:
2019_02_06-PM-03_51_03
Theory : continuity
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