Nuprl Lemma : ndiff_id_r
∀[a:ℕ]. ((a -- 0) = a ∈ ℤ)
Proof
Definitions occuring in Statement :
ndiff: a -- b
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
natural_number: $n
,
int: ℤ
,
equal: s = t ∈ T
Definitions unfolded in proof :
ndiff: a -- b
,
imax: imax(a;b)
,
uall: ∀[x:A]. B[x]
,
has-value: (a)↓
,
member: t ∈ T
,
uimplies: b supposing a
,
nat: ℕ
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
ifthenelse: if b then t else f fi
,
ge: i ≥ j
,
decidable: Dec(P)
,
or: P ∨ Q
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
false: False
,
not: ¬A
,
top: Top
,
prop: ℙ
,
bfalse: ff
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
Lemmas referenced :
value-type-has-value,
int-value-type,
subtract_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
itermSubtract_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
callbyvalueReduce,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination
Latex:
\mforall{}[a:\mBbbN{}]. ((a -- 0) = a)
Date html generated:
2017_04_14-AM-09_14_50
Last ObjectModification:
2017_02_27-PM-03_52_47
Theory : int_2
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