Nuprl Lemma : eval_list-append-nil-is-eval_list
∀[t:Top]. (eval_list(t @ []) ~ eval_list(t))
Proof
Definitions occuring in Statement :
append: as @ bs,
eval_list: eval_list(t),
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
append: as @ bs,
eval_list: eval_list(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict1: strict1(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
list_ind: list_ind,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
guard: {T},
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top,
cons: [a / b]
Lemmas referenced :
sqequal-list_ind,
has-value_wf_base,
base_wf,
is-exception_wf,
eval_list_cons_lemma,
sqle_wf_base,
eval_list_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
baseClosed,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
inlFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inrFormation,
instantiate,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
divergentSqle,
sqleRule,
sqleReflexivity,
because_Cache,
sqequalAxiom
Latex:
\mforall{}[t:Top]. (eval\_list(t @ []) \msim{} eval\_list(t))
Date html generated:
2018_05_21-PM-10_18_44
Last ObjectModification:
2018_05_19-PM-04_13_03
Theory : eval!all
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