Nuprl Lemma : eq_int_eq_false
∀[i,j:ℤ]. (i =z j) = ff supposing i ≠ j
Proof
Definitions occuring in Statement :
eq_int: (i =z j),
bfalse: ff,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
false: False,
sq_type: SQType(T),
all: ∀x:A. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A
Lemmas referenced :
iff_imp_equal_bool,
eq_int_wf,
bfalse_wf,
iff_functionality_wrt_iff,
assert_wf,
equal-wf-base,
int_subtype_base,
false_wf,
iff_weakening_uiff,
assert_of_eq_int,
iff_weakening_equal,
subtype_base_sq,
nequal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
intEquality,
applyEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
lambdaFormation,
promote_hyp,
instantiate,
cumulativity,
dependent_functionElimination,
voidElimination,
Error :universeIsType,
isect_memberEquality,
axiomEquality,
Error :inhabitedIsType
Latex:
\mforall{}[i,j:\mBbbZ{}]. (i =\msubz{} j) = ff supposing i \mneq{} j
Date html generated:
2019_06_20-AM-11_31_44
Last ObjectModification:
2018_09_26-AM-11_24_55
Theory : bool_1
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