Nuprl Lemma : l_all-nil
∀[P:Top]. ((∀x∈[].P[x]) ⇐⇒ True)
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
iff: P ⇐⇒ Q,
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
l_all_wf_nil,
l_all_nil,
true_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberEquality
Latex:
\mforall{}[P:Top]. ((\mforall{}x\mmember{}[].P[x]) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-AM-07_49_45
Last ObjectModification:
2015_12_26-PM-04_45_36
Theory : list_1
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