Nuprl Lemma : last_append_singleton_sq
dumplicate - needes to be removed and references replaced by last_append_singleton⋅
∀[T:Type]. ∀L:T List. ∀a:T. (last(L @ [a]) ~ a)
Proof
Definitions occuring in Statement :
last: last(L),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
top: Top,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
last_singleton_append,
subtype_rel_list,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
lambdaEquality,
because_Cache,
sqequalRule,
sqequalAxiom,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}a:T. (last(L @ [a]) \msim{} a)
Date html generated:
2016_07_08-PM-04_49_15
Last ObjectModification:
2015_12_26-PM-05_06_06
Theory : list_1
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