Nuprl Lemma : atom2-deq-aux
∀[a,b:Atom2]. uiff(a = b ∈ Atom2;↑a =a2 b)
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,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
assert_of_eq_atom2,
assert_witness,
eq_atom_wf2,
equal_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_functionElimination,
atomnEquality,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[a,b:Atom2]. uiff(a = b;\muparrow{}a =a2 b)
Date html generated:
2016_05_14-PM-03_33_46
Last ObjectModification:
2015_12_26-PM-06_00_57
Theory : decidable!equality
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