Nuprl Lemma : rank-option-decompose
∀[P:pi_term()]. pi-rank(P) = ((pi-rank(pioption-left(P)) + pi-rank(pioption-right(P))) + 1) ∈ ℕ supposing ↑pioption?(P)
Proof
Definitions occuring in Statement :
pi-rank: pi-rank(p),
pioption-right: pioption-right(v),
pioption-left: pioption-left(v),
pioption?: pioption?(v),
pi_term: pi_term(),
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Lemmas :
assert_wf,
pioption?_wf,
pi_term_wf,
pi-option-decompose,
rank-option,
pioption-left_wf,
pioption-right_wf,
zero-le-nat,
pi-rank_wf,
squash_wf,
true_wf,
nat_wf,
iff_weakening_equal,
le_wf
Latex:
\mforall{}[P:pi\_term()]
pi-rank(P) = ((pi-rank(pioption-left(P)) + pi-rank(pioption-right(P))) + 1)
supposing \muparrow{}pioption?(P)
Date html generated:
2015_07_23-AM-11_33_12
Last ObjectModification:
2015_02_04-PM-03_43_34
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