Nuprl Lemma : eval-list_wf
∀[L:ℤ List]. (eval-list(L) ∈ {L':ℤ List| L' = L ∈ (ℤ List)} )
Proof
Definitions occuring in Statement :
eval-list: eval-list(L),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eval-list: eval-list(L),
uimplies: b supposing a,
id-fun: id-fun(T),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
norm-list_wf,
int-value-type,
equal-wf-base,
int_subtype_base,
id-fun_wf,
list_wf,
subtype_rel_sets,
list_subtype_base,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
lambdaFormation,
because_Cache,
setElimination,
rename,
setEquality,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[L:\mBbbZ{} List]. (eval-list(L) \mmember{} \{L':\mBbbZ{} List| L' = L\} )
Date html generated:
2017_04_14-AM-09_27_55
Last ObjectModification:
2017_02_27-PM-04_01_05
Theory : list_1
Home
Index