Nuprl Lemma : length-append
∀[as,bs:Top]. (||as @ bs|| ~ ||as|| + ||bs||)
Proof
Definitions occuring in Statement :
length: ||as||,
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
append: as @ bs,
length: ||as||,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict1: strict1(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
list_ind: list_ind,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
guard: {T},
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top
Lemmas referenced :
length-wf-has-value,
zero-add-base,
add-commutes,
add-associates,
top_wf,
sqle_wf_base,
length_of_cons_lemma,
int-value-type,
value-type-has-value,
is-exception_wf,
base_wf,
has-value_wf_base,
sqequal-list_ind
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseClosed,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
inlFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inrFormation,
callbyvalueAdd,
productElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
addExceptionCases,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
natural_numberEquality,
divergentSqle,
sqleRule,
sqleReflexivity
Latex:
\mforall{}[as,bs:Top]. (||as @ bs|| \msim{} ||as|| + ||bs||)
Date html generated:
2016_05_14-AM-06_35_06
Last ObjectModification:
2016_01_14-PM-08_23_09
Theory : list_0
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