Nuprl Lemma : name_eq_symmetry
∀[x,y:Name]. (name_eq(x;y) ~ name_eq(y;x))
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
name: Name,
uall: ∀[x:A]. B[x],
sqequal: s ~ 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,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
name_eq_wf,
equal_wf,
name_wf,
assert-name_eq,
assert_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
equalitySymmetry,
addLevel,
productElimination,
impliesFunctionality,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
independent_functionElimination,
sqequalAxiom,
sqequalRule,
isect_memberEquality
Latex:
\mforall{}[x,y:Name]. (name\_eq(x;y) \msim{} name\_eq(y;x))
Date html generated:
2016_05_14-PM-03_34_31
Last ObjectModification:
2015_12_26-PM-06_00_11
Theory : decidable!equality
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