Nuprl Lemma : rv-partial-sum-unroll
∀[m:ℕ+]. ∀[X:Top]. (rv-partial-sum(m;i.X[i]) ~ rv-partial-sum(m - 1;i.X[i]) + X[m - 1])
Proof
Definitions occuring in Statement :
rv-partial-sum: rv-partial-sum(n;i.X[i]),
rv-add: X + Y,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Lemmas :
top_wf,
nat_plus_wf,
lt_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
less_than_wf,
le_int_wf,
le_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int
\mforall{}[m:\mBbbN{}\msupplus{}]. \mforall{}[X:Top]. (rv-partial-sum(m;i.X[i]) \msim{} rv-partial-sum(m - 1;i.X[i]) + X[m - 1])
Date html generated:
2015_07_17-AM-08_02_24
Last ObjectModification:
2015_01_27-AM-11_21_46
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