Nuprl Lemma : ratsign_wf
∀[x:ℤ × ℕ+]. (ratsign(x) ∈ {-1..2-})
Proof
Definitions occuring in Statement :
ratsign: ratsign(x),
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
minus: -n,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ratsign: ratsign(x),
has-value: (a)↓,
uimplies: b supposing a,
top: Top,
pi1: fst(t),
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,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
value-type-has-value,
int-value-type,
pi1_wf_top,
istype-void,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
productElimination,
independent_pairEquality,
hypothesisEquality,
isect_memberEquality_alt,
voidElimination,
closedConclusion,
natural_numberEquality,
because_Cache,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
dependent_set_memberEquality_alt,
minusEquality,
independent_pairFormation,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
universeIsType,
productIsType,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
axiomEquality
Latex:
\mforall{}[x:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. (ratsign(x) \mmember{} \{-1..2\msupminus{}\})
Date html generated:
2019_10_30-AM-09_35_28
Last ObjectModification:
2019_01_17-AM-10_24_53
Theory : reals
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