Nuprl Lemma : is-list-if-has-value-rec-pair-bot
∀[t:Base]. is-list-if-has-value-rec(<t, ⊥>)
Proof
Definitions occuring in Statement :
is-list-if-has-value-rec: is-list-if-has-value-rec(t),
bottom: ⊥,
uall: ∀[x:A]. B[x],
pair: <a, b>,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
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),
member: t ∈ T,
nat: ℕ,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-it: exposed-it,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
has-value: (a)↓,
pi2: snd(t),
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
le_wf,
nat_properties,
nequal-le-implies,
zero-add,
subtract_wf,
strictness-spread,
strictness-isaxiom,
strictness-decide,
strictness-ispair,
bottom_diverge,
has-value_wf_base,
nat_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
axiomEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
hypothesis_subsumption,
dependent_set_memberEquality,
independent_pairFormation,
baseClosed
Latex:
\mforall{}[t:Base]. is-list-if-has-value-rec(<t, \mbot{}>)
Date html generated:
2018_05_21-PM-10_19_35
Last ObjectModification:
2017_07_26-PM-06_37_04
Theory : eval!all
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