Nuprl Lemma : firstn_append_front_singleton
∀[L:Top List]. ∀a:Top. (firstn(||L @ [a]|| - 1;L @ [a]) ~ L)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
length: ||as||,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
length-singleton,
firstn_append_front,
cons_wf,
top_wf,
nil_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[L:Top List]. \mforall{}a:Top. (firstn(||L @ [a]|| - 1;L @ [a]) \msim{} L)
Date html generated:
2016_05_14-PM-02_08_31
Last ObjectModification:
2015_12_26-PM-05_06_46
Theory : list_1
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