Nuprl Lemma : insert-no-combine_wf
∀[T:Type]. ∀[cmp:comparison(T)]. ∀[x:T]. ∀[L:T List]. (insert-no-combine(cmp;x;L) ∈ T List)
Proof
Definitions occuring in Statement :
insert-no-combine: insert-no-combine(cmp;x;l),
comparison: comparison(T),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
insert-no-combine: insert-no-combine(cmp;x;l),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
comparison: comparison(T),
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x]
Lemmas referenced :
list_ind_wf,
list_wf,
cons_wf,
nil_wf,
ifthenelse_wf,
le_int_wf,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
natural_numberEquality,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[cmp:comparison(T)]. \mforall{}[x:T]. \mforall{}[L:T List]. (insert-no-combine(cmp;x;L) \mmember{} T List)
Date html generated:
2016_05_14-PM-02_43_02
Last ObjectModification:
2015_12_26-PM-02_41_24
Theory : list_1
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