Nuprl Lemma : fun-not-int
∀[f:ℕ+ ⟶ ℤ]. (isint(f) ~ ff)
Proof
Definitions occuring in Statement :
nat_plus: ℕ+,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
isint: isint def,
function: x:A ⟶ B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
exists: ∃x:A. B[x],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
bfalse_wf,
value-type_wf,
int-value-type,
less_than_wf,
nat_plus_wf,
function-not-int,
bool_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
intEquality,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
functionEquality,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (isint(f) \msim{} ff)
Date html generated:
2016_05_18-AM-06_47_54
Last ObjectModification:
2016_01_17-AM-01_45_10
Theory : reals
Home
Index