Nuprl Lemma : trivial-eq
∀[T:Type]. ∀[x:T]. {x = x ∈ T ⇐⇒ True}
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
true: True,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \{x = x \mLeftarrow{}{}\mRightarrow{} True\}
Date html generated:
2017_10_01-AM-09_11_18
Last ObjectModification:
2017_07_26-PM-04_47_22
Theory : general
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