Nuprl Lemma : reduce-bool-bfalse
∀T:Type. ∀f:T ─→ 𝔹 ─→ 𝔹. ∀L:T List. (reduce(λx,b. (b ∧b f[x;b]);ff;L) ~ ff)
Proof
Definitions occuring in Statement :
reduce: reduce(f;k;as),
list: T List,
band: p ∧b q,
bfalse: ff,
bool: 𝔹,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
reduce_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
reduce_cons_lemma,
bool_wf,
bool_subtype_base,
band_commutes,
iff_weakening_equal,
band_ff_simp,
list_wf
\mforall{}T:Type. \mforall{}f:T {}\mrightarrow{} \mBbbB{} {}\mrightarrow{} \mBbbB{}. \mforall{}L:T List. (reduce(\mlambda{}x,b. (b \mwedge{}\msubb{} f[x;b]);ff;L) \msim{} ff)
Date html generated:
2015_07_17-AM-08_36_12
Last ObjectModification:
2015_02_04-AM-07_07_25
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