Nuprl Lemma : modify-combinator2_wf
∀[n:ℕ]. ∀[A:ℕn ⟶ Type]. ∀[m:ℕ].
∀[B:ℕm ⟶ Type]. ∀[T:Type]. ∀[f:(i:ℕn ⟶ (A i + Top)) ⟶ (i:ℕm ⟶ (B i + Top)) ⟶ T].
(modify-combinator2(f) ∈ (i:ℕn ⟶ (A i + Top))
⟶ (i:ℕm - 1 ⟶ if (i =z 0) then one_or_both(B 0;B 1) + Top else B (i + 1) + Top fi )
⟶ T)
supposing 1 < m
Proof
Definitions occuring in Statement :
modify-combinator2: modify-combinator2(f),
int_seg: {i..j-},
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
one_or_both: one_or_both(A;B)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
modify-combinator2: modify-combinator2(f),
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
eq_int: (i =z j),
subtype_rel: A ⊆r B,
subtract: n - m
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[m:\mBbbN{}].
\mforall{}[B:\mBbbN{}m {}\mrightarrow{} Type]. \mforall{}[T:Type]. \mforall{}[f:(i:\mBbbN{}n {}\mrightarrow{} (A i + Top)) {}\mrightarrow{} (i:\mBbbN{}m {}\mrightarrow{} (B i + Top)) {}\mrightarrow{} T].
(modify-combinator2(f) \mmember{} (i:\mBbbN{}n {}\mrightarrow{} (A i + Top))
{}\mrightarrow{} (i:\mBbbN{}m - 1 {}\mrightarrow{} if (i =\msubz{} 0) then one\_or\_both(B 0;B 1) + Top else B (i + 1) + Top fi )
{}\mrightarrow{} T)
supposing 1 < m
Date html generated:
2016_05_16-AM-10_10_54
Last ObjectModification:
2016_01_17-PM-01_23_20
Theory : new!event-ordering
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