Nuprl Lemma : eq_atom-reflexive
∀[x:Atom]. x =a x = tt
Proof
Definitions occuring in Statement :
eq_atom: x =a y,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
iff_imp_equal_bool,
eq_atom_wf,
btrue_wf,
equal_wf,
true_wf,
assert_of_eq_atom,
assert_wf,
iff_wf,
member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
atomEquality,
addLevel,
productElimination,
impliesFunctionality,
because_Cache
Latex:
\mforall{}[x:Atom]. x =a x = tt
Date html generated:
2016_05_13-PM-03_56_50
Last ObjectModification:
2015_12_26-AM-10_52_02
Theory : bool_1
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