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
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\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:
2016_05_16-AM-09_18_00
Last ObjectModification:
2016_01_17-PM-01_30_56
Theory : new!event-ordering
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