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]
Lemmas :
pi_term-induction,
all_wf,
l_member_wf,
pi-choices_wf,
less_than_wf,
pi-rank_wf,
nat_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
pi_prefix_wf,
pi_term_wf,
nil_wf,
btrue_neq_bfalse,
set_wf,
member_singleton,
cons_wf,
member_append,
append_wf,
name_wf,
member-less_than,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add-mul-special,
zero-mul,
add-zero,
add-associates,
le-add-cancel
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:
2015_07_23-AM-11_33_58
Last ObjectModification:
2015_01_29-AM-00_55_31
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