Nuprl Lemma : is-list-if-has-value-rec-snd
∀[t:Base]. (is-list-if-has-value-rec(snd(t))) supposing (is-list-if-has-value-rec(t) and (t ~ <fst(t), snd(t)>))
Proof
Definitions occuring in Statement :
is-list-if-has-value-rec: is-list-if-has-value-rec(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
pair: <a, b>,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
is-list-if-has-value-rec: is-list-if-has-value-rec(t),
is-list-if-has-value-fun: is-list-if-has-value-fun(t;n),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
has-value: (a)↓,
pi2: snd(t),
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
primrec-unroll,
nat_wf,
is-list-if-has-value-rec_wf,
base_wf,
eq_int_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
has-value_wf_base,
is-exception_wf,
add-subtract-cancel,
is-list-if-has-value-fun-ax-mem,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
sqequalAxiom,
hypothesis,
thin,
rename,
sqequalHypSubstitution,
sqequalRule,
isectElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
hypothesisEquality,
natural_numberEquality,
extract_by_obid,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
equalityTransitivity,
equalitySymmetry,
divergentSqle,
sqleReflexivity,
instantiate,
cumulativity,
independent_functionElimination,
productElimination,
lambdaFormation,
impliesFunctionality
Latex:
\mforall{}[t:Base]
(is-list-if-has-value-rec(snd(t))) supposing
(is-list-if-has-value-rec(t) and
(t \msim{} <fst(t), snd(t)>))
Date html generated:
2018_05_21-PM-10_19_32
Last ObjectModification:
2017_07_26-PM-06_37_03
Theory : eval!all
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