Nuprl Lemma : make-strict_wf
∀[alpha:ℕ ⟶ ℕ]. (make-strict(alpha) ∈ StrictInc)
Proof
Definitions occuring in Statement :
make-strict: make-strict(alpha),
strict-inc: StrictInc,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
make-strict: make-strict(alpha),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
primrec: primrec(n;b;c),
less_than: a < b,
squash: ↓T
Lemmas referenced :
primrec_wf,
nat_wf,
false_wf,
le_wf,
lt_int_wf,
nat_properties,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
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,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
int_seg_wf,
implies-strict-inc,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
member-less_than,
primrec1_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtract-add-cancel,
primrec0_lemma,
decidable__lt,
primrec-unroll,
add-subtract-cancel,
le_weakening2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
applyEquality,
functionExtensionality,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
addEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
axiomEquality,
functionEquality,
intWeakElimination,
imageElimination
Latex:
\mforall{}[alpha:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (make-strict(alpha) \mmember{} StrictInc)
Date html generated:
2018_05_21-PM-01_20_31
Last ObjectModification:
2018_05_19-AM-06_33_20
Theory : continuity
Home
Index