Nuprl Lemma : evalall-append-nil
∀[l:Base]. evalall(l @ []) ~ l supposing (evalall(l @ []))↓
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
has-value: (a)↓,
evalall: evalall(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
top: Top,
evalall: evalall(t),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
not: ¬A,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+,
has-value: (a)↓,
outl: outl(x),
outr: outr(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
pi2: snd(t),
bfalse: ff,
it: ⋅,
nil: [],
list_ind: list_ind
Lemmas referenced :
list_ind_nil_lemma,
has-value-implies-dec-isaxiom,
isaxiom-append-nil,
assert_of_bnot,
bfalse_wf,
btrue_wf,
sqeqff_to_assert,
ispair-or-isaxiom-append-nil,
is-exception_wf,
evalall-sqequal,
pi1_cons_lemma,
list_ind_cons_lemma,
pair-eta,
prod-if-ispair-append-nil,
pi2-if-ispair-append-nil,
pi1-if-ispair-append-nil,
has-value-implies-dec-isinr-2,
has-value-implies-dec-isinl-2,
top_wf,
has-value-implies-dec-ispair-2,
fun_exp_unroll_1,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-ge-2,
false_wf,
subtract_wf,
decidable__le,
bottom_diverge,
strictness-apply,
fun_exp0_lemma,
int_subtype_base,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties,
append-nil-sqle,
evalall-sqle,
base_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
sqleTransitivity,
voidElimination,
voidEquality,
compactness,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_functionElimination,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
applyEquality,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
intEquality,
minusEquality,
dependent_set_memberEquality,
callbyvalueCallbyvalue,
callbyvalueReduce,
sqleRule,
divergentSqle,
sqleReflexivity,
ispairCases,
isinlCases,
isinrCases,
exceptionSqequal
Latex:
\mforall{}[l:Base]. evalall(l @ []) \msim{} l supposing (evalall(l @ []))\mdownarrow{}
Date html generated:
2016_05_14-AM-06_32_35
Last ObjectModification:
2016_01_14-PM-08_27_24
Theory : list_0
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