Nuprl Lemma : list_update_length
∀[l:Top List]. ∀[i:ℤ]. ∀[x:Top]. (||l[i:=x]|| ~ ||l||)
Proof
Definitions occuring in Statement :
list_update: l[i:=x],
length: ||as||,
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_update: l[i:=x],
top: Top,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
top_wf,
list_wf,
mklist_length,
length_wf_nat,
length_wf,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
intEquality,
voidElimination,
voidEquality,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[l:Top List]. \mforall{}[i:\mBbbZ{}]. \mforall{}[x:Top]. (||l[i:=x]|| \msim{} ||l||)
Date html generated:
2016_05_15-PM-03_49_37
Last ObjectModification:
2015_12_27-PM-01_22_32
Theory : general
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