Nuprl Lemma : pi-par-decompose
∀[P:pi_term()]. P = pipar(pipar-left(P);pipar-right(P)) ∈ pi_term() supposing ↑pipar?(P)
Proof
Definitions occuring in Statement :
pipar-right: pipar-right(v),
pipar-left: pipar-left(v),
pipar?: pipar?(v),
pipar: pipar(left;right),
pi_term: pi_term(),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
pizero: pizero(),
pi_term_size: pi_term_size(p),
pipar?: pipar?(v),
pi1: fst(t),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
picomm: picomm(pre;body),
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
pioption: pioption(left;right),
pipar: pipar(left;right),
pipar-left: pipar-left(v),
pi2: snd(t),
pipar-right: pipar-right(v),
true: True,
pirep: pirep(body),
pinew: pinew(name;body)
Latex:
\mforall{}[P:pi\_term()]. P = pipar(pipar-left(P);pipar-right(P)) supposing \muparrow{}pipar?(P)
Date html generated:
2016_05_17-AM-11_23_06
Last ObjectModification:
2016_01_18-AM-07_49_51
Theory : event-logic-applications
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