Nuprl Lemma : rank-option
∀[P,Q:pi_term()]. (pi-rank(pioption(P;Q)) = ((pi-rank(P) + pi-rank(Q)) + 1) ∈ ℕ)
Proof
Definitions occuring in Statement :
pi-rank: pi-rank(p),
pioption: pioption(left;right),
pi_term: pi_term(),
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-rank: pi-rank(p),
pioption: pioption(left;right),
pi_term_ind: pi_term_ind(v;zero;pre,body,rec1....;left,right,rec2,rec3....;left,right,rec4,rec5....;body,rec6....;name,body,rec7....),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
guard: {T},
ge: i ≥ j ,
uiff: uiff(P;Q)
Latex:
\mforall{}[P,Q:pi\_term()]. (pi-rank(pioption(P;Q)) = ((pi-rank(P) + pi-rank(Q)) + 1))
Date html generated:
2016_05_17-AM-11_23_47
Last ObjectModification:
2016_01_18-AM-07_48_34
Theory : event-logic-applications
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