Nuprl Lemma : eq_atom_eq_false_elim_sqequal
∀[x,y:Atom]. ¬(x = y ∈ Atom) supposing x =a y ~ ff
Proof
Definitions occuring in Statement :
eq_atom: x =a y,
bfalse: ff,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
atom: Atom,
sqequal: s ~ t,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
nequal: a ≠ b ∈ T ,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
assert_of_ff,
neg_assert_of_eq_atom,
equal-wf-base,
atom_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
voidElimination,
atomEquality,
applyEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:Atom]. \mneg{}(x = y) supposing x =a y \msim{} ff
Date html generated:
2017_04_14-AM-07_36_35
Last ObjectModification:
2017_02_27-PM-03_08_42
Theory : subtype_1
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