Nuprl Lemma : neg_assert_of_eq_atom1
∀[x,y:Atom1]. uiff(¬↑x =a1 y;x ≠ y ∈ Atom1 )
Proof
Definitions occuring in Statement :
eq_atom: eq_atom$n(x;y),
atom: Atom$n,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nequal: a ≠ b ∈ T ,
false: False
Lemmas referenced :
assert_of_eq_atom1,
equal-wf-base,
atom1_subtype_base,
not_wf,
assert_wf,
eq_atom_wf1,
nequal_wf,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
addLevel,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
atomnEquality,
applyEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
voidElimination,
instantiate,
cumulativity,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:Atom1]. uiff(\mneg{}\muparrow{}x =a1 y;x \mneq{} y \mmember{} Atom1 )
Date html generated:
2017_04_14-AM-07_14_35
Last ObjectModification:
2017_02_27-PM-02_50_15
Theory : atom_1
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