Nuprl Lemma : select_fun_last_partial_ap_gen1
∀[g:Base]. ∀[m1,m2:ℕ]. (select_fun_last(partial_ap_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2) ~ select_fun_last(g;m1 + m2))
Proof
Definitions occuring in Statement :
select_fun_last: select_fun_last(g;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
select_fun_last: select_fun_last(g;m)
Lemmas referenced :
select_fun_ap_is_last1,
nat_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:Base]. \mforall{}[m1,m2:\mBbbN{}].
(select\_fun\_last(partial\_ap\_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2) \msim{} select\_fun\_last(g;m1 + m2))
Date html generated:
2016_05_15-PM-02_11_54
Last ObjectModification:
2015_12_27-AM-00_34_24
Theory : untyped!computation
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