Nuprl Lemma : 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]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
btrue: tt
, 
not: ¬A
, 
eq_atom: eq_atom$n(x;y)
, 
bfalse: ff
, 
or: P ∨ Q
, 
decidable: Dec(P)
, 
subtype_rel: A ⊆r B
, 
false: False
, 
true: True
, 
bool: 𝔹
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
ifthenelse: if b then t else f fi 
, 
assert: ↑b
, 
prop: ℙ
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
uiff: uiff(P;Q)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
decidable__atom_equal_1, 
atom1_subtype_base, 
equal-wf-base, 
equal_wf, 
false_wf, 
true_wf, 
bool_wf, 
eq_atom_wf1, 
assert_wf
Rules used in proof : 
atomn_eqReduceTrueSq, 
natural_numberEquality, 
atomn_eqReduceFalseSq, 
because_Cache, 
isect_memberEquality, 
independent_pairEquality, 
productElimination, 
applyEquality, 
atomnEquality, 
independent_functionElimination, 
dependent_functionElimination, 
voidElimination, 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
unionElimination, 
lambdaFormation, 
sqequalRule, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
hypothesis, 
independent_pairFormation, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[x,y:Atom1].    uiff(\muparrow{}x  =a1  y;x  =  y)
Date html generated:
2018_07_25-PM-01_27_27
Last ObjectModification:
2018_07_18-PM-00_17_25
Theory : atom_1
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