Nuprl Lemma : pi-rank-pi-replace
∀[t,x:Name]. ∀[P:pi_term()]. (pi-rank(pi-replace(t;x;P)) = pi-rank(P) ∈ ℤ)
Proof
Definitions occuring in Statement :
pi-replace: pi-replace(t;x;P),
pi-rank: pi-rank(p),
pi_term: pi_term(),
name: Name,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
pi_term-induction,
equal_wf,
pi-rank_wf,
pi-replace_wf,
nat_wf,
pizero_wf,
pi_prefix_wf,
pi_term_wf,
name_wf
Latex:
\mforall{}[t,x:Name]. \mforall{}[P:pi\_term()]. (pi-rank(pi-replace(t;x;P)) = pi-rank(P))
Date html generated:
2015_07_23-AM-11_33_30
Last ObjectModification:
2015_01_29-AM-00_55_11
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