Nuprl Lemma : neg_assert_of_eq_atom
∀[x,y:Atom]. uiff(¬↑x =a y;x ≠ y ∈ Atom )
Proof
Definitions occuring in Statement :
assert: ↑b,
eq_atom: x =a y,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A,
atom: Atom
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
guard: {T},
iff: P ⇐⇒ Q,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_weakening_uiff,
not_wf,
assert_wf,
eq_atom_wf,
equal-wf-base,
atom_subtype_base,
not_functionality_wrt_uiff,
assert_of_eq_atom,
nequal_wf
Rules used in proof :
cut,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
productElimination,
thin,
independent_pairFormation,
Error :isect_memberFormation_alt,
introduction,
independent_isectElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
atomEquality,
applyEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
lambdaEquality,
dependent_functionElimination,
voidElimination,
instantiate,
cumulativity,
Error :universeIsType,
Error :inhabitedIsType,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:Atom]. uiff(\mneg{}\muparrow{}x =a y;x \mneq{} y \mmember{} Atom )
Date html generated:
2019_06_20-AM-11_31_31
Last ObjectModification:
2018_09_26-AM-11_24_50
Theory : bool_1
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