Nuprl Lemma : set-equal-reflex
∀[T:Type]. ∀[x:T List]. set-equal(T;x;x)
Proof
Definitions occuring in Statement :
set-equal: set-equal(T;x;y),
list: T List,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
set-equal: set-equal(T;x;y),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T List]. set-equal(T;x;x)
Date html generated:
2016_05_14-PM-01_37_21
Last ObjectModification:
2015_12_26-PM-05_28_09
Theory : list_1
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