Nuprl Lemma : sqle-append-nil-if-has-value
∀[t:Base]. t ≤ t @ [] supposing (t)↓ ⇒ (is-list(t))↓
Proof
Definitions occuring in Statement :
is-list: is-list(t),
append: as @ bs,
nil: [],
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
append: as @ bs,
list_ind: list_ind,
uall: ∀[x:A]. B[x],
prop: ℙ,
uimplies: b supposing a,
is-list: is-list(t),
sq_stable: SqStable(P),
nat: ℕ,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
has-value: (a)↓,
cons: [a / b],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
pi2: snd(t),
it: ⋅,
nil: [],
squash: ↓T,
guard: {T}
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
base_wf,
sq_stable__sqle,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
int_subtype_base,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
fun_exp_unroll_1,
has-value-implies-dec-ispair,
list_ind_cons_lemma,
has-value-implies-dec-isaxiom,
list_ind_nil_lemma
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
exceptionSqequal,
hypothesis,
axiomSqleEquality,
sqequalRule,
divergentSqle,
sqleReflexivity,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
isect_memberFormation,
independent_functionElimination,
compactness,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
applyEquality,
because_Cache,
unionElimination,
dependent_set_memberEquality,
callbyvalueReduce,
sqleRule,
imageMemberEquality,
imageElimination,
functionEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[t:Base]. t \mleq{} t @ [] supposing (t)\mdownarrow{} {}\mRightarrow{} (is-list(t))\mdownarrow{}
Date html generated:
2019_10_16-AM-11_38_07
Last ObjectModification:
2018_08_15-PM-03_49_28
Theory : eval!all
Home
Index