Nuprl Lemma : neg_assert_of_eq_int
∀[x,y:ℤ]. uiff(¬↑(x =z y);x ≠ y)
Proof
Definitions occuring in Statement :
assert: ↑b,
eq_int: (i =z j),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal-wf-base,
int_subtype_base,
not_wf,
assert_wf,
eq_int_wf,
nequal_wf,
iff_weakening_uiff,
not_functionality_wrt_uiff,
assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
extract_by_obid,
intEquality,
applyEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
voidElimination,
Error :universeIsType,
independent_pairFormation,
independent_isectElimination,
independent_functionElimination,
instantiate,
cumulativity
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(\mneg{}\muparrow{}(x =\msubz{} y);x \mneq{} y)
Date html generated:
2019_06_20-AM-11_31_29
Last ObjectModification:
2018_09_26-AM-11_24_48
Theory : bool_1
Home
Index