Nuprl Lemma : nil_iseg
∀[T:Type]. ∀l:T List. [] ≤ l
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
append: as @ bs,
list_ind: list_ind,
nil: [],
it: ⋅,
prop: ℙ
Lemmas referenced :
equal_wf,
list_wf,
append_wf,
nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
hypothesisEquality,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l:T List. [] \mleq{} l
Date html generated:
2016_05_14-PM-01_31_57
Last ObjectModification:
2015_12_26-PM-05_24_48
Theory : list_1
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