Nuprl Lemma : add-nat-missing_wf
∀[i:ℕ]. ∀[s:nat-missing-type()]. (add-nat-missing(i;s) ∈ nat-missing-type())
Proof
Definitions occuring in Statement :
add-nat-missing: add-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,
add-nat-missing: add-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
nat: ℕ,
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,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[i:\mBbbN{}]. \mforall{}[s:nat-missing-type()]. (add-nat-missing(i;s) \mmember{} nat-missing-type())
Date html generated:
2016_05_17-PM-01_45_18
Last ObjectModification:
2016_01_17-AM-11_37_59
Theory : datatype-signatures
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