Nuprl Lemma : ml-absval_wf
∀[x:ℤ]. (ml-absval(x) ∈ ℤ)
Proof
Definitions occuring in Statement :
ml-absval: ml-absval(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ml-absval: ml-absval(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
prop: ℙ
Lemmas referenced :
ml_apply_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
equal_wf,
int-valueall-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
lambdaEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
minusEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[x:\mBbbZ{}]. (ml-absval(x) \mmember{} \mBbbZ{})
Date html generated:
2017_09_29-PM-05_51_41
Last ObjectModification:
2017_05_22-PM-02_09_47
Theory : ML
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