Nuprl Lemma : bool-cmp-zero
∀[x,y:𝔹]. uiff((bool-cmp() x y) = 0 ∈ ℤ;x = y)
Proof
Definitions occuring in Statement :
bool-cmp: bool-cmp(),
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bool-cmp: bool-cmp(),
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
true: True,
false: False,
not: ¬A,
subtype_rel: A ⊆r B,
comparison: comparison(T)
Lemmas referenced :
btrue_wf,
equal_wf,
bool_wf,
subtype_base_sq,
int_subtype_base,
btrue_neq_bfalse,
bfalse_wf,
bool-cmp_wf,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
sqequalRule,
independent_pairFormation,
lemma_by_obid,
hypothesis,
isectElimination,
intEquality,
natural_numberEquality,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp,
productElimination,
independent_pairEquality,
isect_memberEquality,
hypothesisEquality,
axiomEquality,
applyEquality,
because_Cache,
minusEquality,
lambdaEquality,
setElimination,
rename
Latex:
\mforall{}[x,y:\mBbbB{}]. uiff((bool-cmp() x y) = 0;x = y)
Date html generated:
2016_05_14-PM-02_37_00
Last ObjectModification:
2015_12_26-PM-04_18_06
Theory : list_1
Home
Index