Nuprl Lemma : list_accum_cons
∀[A,B,y,f:Top].
(accumulate (with value x and list item a):
f[x;a]
over list:
[A / B]
with starting value:
y) ~ accumulate (with value x and list item a):
f[x;a]
over list:
B
with starting value:
f[y;A]))
Proof
Definitions occuring in Statement :
list_accum: list_accum,
cons: [a / b],
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_accum_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[A,B,y,f:Top].
(accumulate (with value x and list item a):
f[x;a]
over list:
[A / B]
with starting value:
y) \msim{} accumulate (with value x and list item a):
f[x;a]
over list:
B
with starting value:
f[y;A]))
Date html generated:
2016_05_14-AM-06_29_15
Last ObjectModification:
2015_12_26-PM-00_40_24
Theory : list_0
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