Nuprl Lemma : assert_of_eq_atom2
∀[x,y:Atom2]. uiff(↑x =a2 y;x = y ∈ Atom2)
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],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
true: True,
false: False,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
bfalse: ff,
eq_atom: eq_atom$n(x;y),
not: ¬A,
btrue: tt
Lemmas referenced :
assert_wf,
eq_atom_wf2,
bool_wf,
true_wf,
false_wf,
equal_wf,
equal-wf-base,
atom2_subtype_base,
decidable__atom_equal_2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaFormation,
unionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
dependent_functionElimination,
independent_functionElimination,
atomnEquality,
applyEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
atomn_eqReduceFalseSq,
natural_numberEquality,
atomn_eqReduceTrueSq
Latex:
\mforall{}[x,y:Atom2]. uiff(\muparrow{}x =a2 y;x = y)
Date html generated:
2017_04_14-AM-07_14_34
Last ObjectModification:
2017_02_27-PM-02_50_11
Theory : atom_1
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