Nuprl Lemma : pi-level-pi-replace
∀[t,x:Name]. ∀[P:pi_term()]. (pi-level(pi-replace(t;x;P)) = pi-level(P) ∈ ℤ)
Proof
Definitions occuring in Statement :
pi-replace: pi-replace(t;x;P),
pi-level: pi-level(p),
pi_term: pi_term(),
name: Name,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
implies: P ⇒ Q,
pi-level: pi-level(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-replace: pi-replace(t;x;P),
pizero: pizero(),
all: ∀x:A. B[x],
picomm: picomm(pre;body),
prop: ℙ,
pioption: pioption(left;right),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
pipar: pipar(left;right),
pirep: pirep(body),
pinew: pinew(name;body),
let: let
Latex:
\mforall{}[t,x:Name]. \mforall{}[P:pi\_term()]. (pi-level(pi-replace(t;x;P)) = pi-level(P))
Date html generated:
2016_05_17-AM-11_24_43
Last ObjectModification:
2016_01_18-AM-07_48_08
Theory : event-logic-applications
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