Nuprl Lemma : remove-nat-missing_wf
∀[i:ℕ]. ∀[s:nat-missing-type()]. (remove-nat-missing(i;s) ∈ nat-missing-type())
Proof
Definitions occuring in Statement :
remove-nat-missing: remove-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat-missing-type: nat-missing-type(),
remove-nat-missing: remove-nat-missing(i;s),
and: P ∧ Q,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
has-value: (a)↓,
le: A ≤ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T ,
l_member: (x ∈ l),
less_than: a < b,
squash: ↓T,
last: last(L),
l-ordered: l-ordered(T;x,y.R[x; y];L),
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
int_seg: {i..j-},
lelt: i ≤ j < k,
increasing: increasing(f;k),
subtract: n - m,
select: L[n],
cons: [a / b],
eq_int: (i =z j),
less_than': less_than'(a;b),
int-minus-comparison-inc: int-minus-comparison-inc(f),
comparison: comparison(T)
Latex:
\mforall{}[i:\mBbbN{}]. \mforall{}[s:nat-missing-type()]. (remove-nat-missing(i;s) \mmember{} nat-missing-type())
Date html generated:
2016_05_17-PM-01_45_55
Last ObjectModification:
2016_01_17-AM-11_38_12
Theory : datatype-signatures
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