Nuprl Lemma : equiv_rel_true
∀[T:Type]. EquivRel(T;x,y.True)
Proof
Definitions occuring in Statement :
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
true: True,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
hypothesisEquality,
lemma_by_obid,
hypothesis,
because_Cache,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. EquivRel(T;x,y.True)
Date html generated:
2016_05_13-PM-04_14_58
Last ObjectModification:
2015_12_26-AM-11_30_06
Theory : rel_1
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