Nuprl Lemma : sign-squared
∀[x:ℤ]. ((sign(x) * sign(x)) = 1 ∈ ℤ)
Proof
Definitions occuring in Statement :
sign: sign(x),
uall: ∀[x:A]. B[x],
multiply: n * m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sign: sign(x),
member: t ∈ T,
subtype_rel: A ⊆r B,
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,
prop: ℙ,
false: False,
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 ,
bfalse: ff,
guard: {T}
Lemmas referenced :
le_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermMultiply_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
lt_int_wf,
less_than_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
hypothesis,
intEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
minusEquality,
lambdaFormation,
equalityElimination,
independent_functionElimination,
productElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbZ{}]. ((sign(x) * sign(x)) = 1)
Date html generated:
2017_04_17-AM-09_45_32
Last ObjectModification:
2017_02_27-PM-05_40_00
Theory : num_thy_1
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