Nuprl Lemma : eq_atom_eq_false_elim
∀[x,y:Atom]. ¬(x = y ∈ Atom) supposing x =a y = ff
Proof
Definitions occuring in Statement :
eq_atom: x =a y,
bfalse: ff,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
equal-wf-base,
atom_subtype_base,
bool_wf,
assert_wf,
bnot_wf,
eq_atom_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
assert_of_eq_atom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
atomEquality,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
productElimination,
independent_isectElimination
Latex:
\mforall{}[x,y:Atom]. \mneg{}(x = y) supposing x =a y = ff
Date html generated:
2019_06_20-AM-11_33_15
Last ObjectModification:
2018_09_26-PM-00_12_08
Theory : int_1
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