Nuprl Lemma : eval_list-sqle-append-nil
∀[t:Base]. eval_list(t) ≤ t @ [] supposing ¬is-exception(eval_list(t))
Proof
Definitions occuring in Statement :
append: as @ bs,
eval_list: eval_list(t),
nil: [],
is-exception: is-exception(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
islist: islist(t),
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
append-nil,
eval_list_sq,
top_wf,
subtype_rel_list,
islist-implies-is-list,
base_wf,
not_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
divergentSqle,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
lemma_by_obid,
isectElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
axiomSqleEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
applyEquality,
lambdaEquality,
voidEquality,
sqleReflexivity
Latex:
\mforall{}[t:Base]. eval\_list(t) \mleq{} t @ [] supposing \mneg{}is-exception(eval\_list(t))
Date html generated:
2016_05_15-PM-10_07_25
Last ObjectModification:
2016_01_16-PM-04_08_41
Theory : eval!all
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