Nuprl Lemma : pi-rank-pi-simple-subst-aux
∀[P:pi_term()]. ∀[t,x:Name]. ∀[avoid:Name List]. (pi-rank(pi-simple-subst-aux(t;x;P;avoid)) = pi-rank(P) ∈ ℤ)
Proof
Definitions occuring in Statement :
pi-simple-subst-aux: pi-simple-subst-aux(t;x;P;avoid),
pi-rank: pi-rank(p),
pi_term: pi_term(),
name: Name,
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
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,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
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-rank: pi-rank(p),
pi_term_ind: pi_term_ind(v;zero;pre,body,rec1....;left,right,rec2,rec3....;left,right,rec4,rec5....;body,rec6....;name,body,rec7....),
pi-simple-subst-aux: pi-simple-subst-aux(t;x;P;avoid),
ycomb: Y,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
picomm: picomm(pre;body),
pioption: pioption(left;right),
pipar: pipar(left;right),
pirep: pirep(body),
pinew: pinew(name;body),
pisend: pisend(chan;var),
pi_prefix_ind: pi_prefix_ind,
let: let,
pircv: pircv(chan;var),
squash: ↓T,
true: True
Latex:
\mforall{}[P:pi\_term()]. \mforall{}[t,x:Name]. \mforall{}[avoid:Name List].
(pi-rank(pi-simple-subst-aux(t;x;P;avoid)) = pi-rank(P))
Date html generated:
2016_05_17-AM-11_25_13
Last ObjectModification:
2016_01_18-AM-07_49_19
Theory : event-logic-applications
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