Nuprl Lemma : rank-par-decompose
∀[P:pi_term()]. pi-rank(P) = ((pi-rank(pipar-left(P)) + pi-rank(pipar-right(P))) + 1) ∈ ℕ supposing ↑pipar?(P)
Proof
Definitions occuring in Statement :
pi-rank: pi-rank(p),
pipar-right: pipar-right(v),
pipar-left: pipar-left(v),
pipar?: pipar?(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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
nat: ℕ,
guard: {T},
ge: i ≥ j ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[P:pi\_term()]
pi-rank(P) = ((pi-rank(pipar-left(P)) + pi-rank(pipar-right(P))) + 1) supposing \muparrow{}pipar?(P)
Date html generated:
2016_05_17-AM-11_23_57
Last ObjectModification:
2016_01_18-AM-07_48_28
Theory : event-logic-applications
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