Nuprl Lemma : last_singleton_append
∀[x:Top]. ∀y:Top List. (last(y @ [x]) ~ x)
Proof
Definitions occuring in Statement :
last: last(L),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
top: Top,
false: False,
prop: ℙ
Lemmas referenced :
last_append,
cons_wf,
top_wf,
nil_wf,
assert_elim,
null_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
assert_wf,
last_singleton2,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
addLevel,
levelHypothesis,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
lambdaEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[x:Top]. \mforall{}y:Top List. (last(y @ [x]) \msim{} x)
Date html generated:
2016_05_14-PM-01_37_04
Last ObjectModification:
2015_12_26-PM-05_27_46
Theory : list_1
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