Nuprl Lemma : singleton-nat-missing-prop
∀x,y:ℕ. (↑member-nat-missing(x;singleton-nat-missing(y)) ⇐⇒ x = y ∈ ℕ)
Proof
Definitions occuring in Statement :
singleton-nat-missing: singleton-nat-missing(i),
member-nat-missing: member-nat-missing(i;s),
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
singleton-nat-missing: singleton-nat-missing(i),
pi1: fst(t),
pi2: snd(t),
not: ¬A,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
prop: ℙ,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
rev_implies: P ⇐ Q,
cand: A c∧ B,
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}x,y:\mBbbN{}. (\muparrow{}member-nat-missing(x;singleton-nat-missing(y)) \mLeftarrow{}{}\mRightarrow{} x = y)
Date html generated:
2016_05_17-PM-01_45_14
Last ObjectModification:
2016_01_17-AM-11_37_09
Theory : datatype-signatures
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