Nuprl Lemma : nat2int_wf
∀[n:ℕ]. (nat2int(n) ∈ ℤ)
Proof
Definitions occuring in Statement :
nat2int: nat2int(m),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat2int: nat2int(m),
nat: ℕ,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
istype-int,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
remainderEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
hypothesis,
closedConclusion,
natural_numberEquality,
Error :lambdaFormation_alt,
instantiate,
extract_by_obid,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
Error :equalityIstype,
baseClosed,
sqequalBase,
Error :inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
int_eqReduceTrueSq,
divideEquality,
Error :dependent_pairFormation_alt,
hypothesisEquality,
promote_hyp,
int_eqReduceFalseSq,
minusEquality,
addEquality,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (nat2int(n) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-PM-02_52_11
Last ObjectModification:
2019_02_06-PM-06_50_24
Theory : continuity
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