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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