Nuprl Lemma : rank-pi-choices
∀[P:pi_term()]. ∀[choice:{c:pi_prefix() × pi_term()| (c ∈ pi-choices(P))} ]. pi-rank(snd(choice)) < pi-rank(P)
Proof
Definitions occuring in Statement :
pi-choices: pi-choices(t),
pi-rank: pi-rank(p),
pi_term: pi_term(),
pi_prefix: pi_prefix(),
l_member: (x ∈ l),
less_than: a < b,
uall: ∀[x:A]. B[x],
pi2: snd(t),
set: {x:A| B[x]} ,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
pi-rank: pi-rank(p),
pi-choices: pi-choices(t),
pizero: pizero(),
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],
uimplies: b supposing a,
not: ¬A,
false: False,
picomm: picomm(pre;body),
iff: P ⇐⇒ Q,
and: P ∧ Q,
pioption: pioption(left;right),
pipar: pipar(left;right),
pirep: pirep(body),
pinew: pinew(name;body),
guard: {T},
nat: ℕ,
pi2: snd(t),
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
ge: i ≥ j
Latex:
\mforall{}[P:pi\_term()]. \mforall{}[choice:\{c:pi\_prefix() \mtimes{} pi\_term()| (c \mmember{} pi-choices(P))\} ].
pi-rank(snd(choice)) < pi-rank(P)
Date html generated:
2016_05_17-AM-11_25_53
Last ObjectModification:
2016_01_18-AM-07_48_24
Theory : event-logic-applications
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