Nuprl Lemma : assert-in-missing-nat
∀i:ℕ. ∀missing:ℕ List. ((↑in-missing(i;missing)) ⇒ (i ∈ missing))
Proof
Definitions occuring in Statement :
in-missing: in-missing(i;missing),
l_member: (x ∈ l),
list: T List,
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
in-missing: in-missing(i;missing),
reduce: reduce(f;k;as),
list_ind: list_ind,
nil: [],
it: ⋅,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
uiff: uiff(P;Q),
or: P ∨ Q,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
guard: {T}
Latex:
\mforall{}i:\mBbbN{}. \mforall{}missing:\mBbbN{} List. ((\muparrow{}in-missing(i;missing)) {}\mRightarrow{} (i \mmember{} missing))
Date html generated:
2016_05_17-PM-01_44_46
Last ObjectModification:
2016_01_17-AM-11_37_22
Theory : datatype-signatures
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