Nuprl Lemma : hd-append-sq
∀[L1:Top List+]. ∀[L2:Top]. (hd(L1 @ L2) ~ hd(L1))
Proof
Definitions occuring in Statement :
listp: A List+,
hd: hd(l),
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
all: ∀x:A. B[x],
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False,
cons: [a / b]
Lemmas referenced :
listp_properties,
top_wf,
list-cases,
length_of_nil_lemma,
list_ind_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
list_ind_cons_lemma,
reduce_hd_cons_lemma,
listp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_functionElimination,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
sqequalAxiom
Latex:
\mforall{}[L1:Top List\msupplus{}]. \mforall{}[L2:Top]. (hd(L1 @ L2) \msim{} hd(L1))
Date html generated:
2016_05_14-PM-03_05_38
Last ObjectModification:
2015_12_26-PM-01_53_16
Theory : list_1
Home
Index