Nuprl Lemma : bar-delay-equal
∀[T:Type]. ∀x:bar-base(T). bar-equal(T;x;bar-delay(x))
Proof
Definitions occuring in Statement :
bar-equal: bar-equal(T;x;y),
bar-delay: bar-delay(b),
bar-base: bar-base(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
bar-equal: bar-equal(T;x;y),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
bar-converges: x↓a,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
bar-delay: bar-delay(b),
bar-val: bar-val(n;x),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
bar-converges_wf,
bar-delay_wf,
bar-base_wf,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_wf,
equal_wf,
unit_wf2,
bar-val_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_antisymmetry_iff,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-subtract-cancel,
int_subtype_base,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
subtract_wf,
not-equal-2,
minus-zero,
minus-minus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
dependent_pairFormation,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
voidElimination,
independent_functionElimination,
independent_isectElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidEquality,
intEquality,
because_Cache,
minusEquality,
unionEquality,
inlEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
applyLambdaEquality,
impliesFunctionality
Latex:
\mforall{}[T:Type]. \mforall{}x:bar-base(T). bar-equal(T;x;bar-delay(x))
Date html generated:
2017_04_14-AM-07_46_11
Last ObjectModification:
2017_02_27-PM-03_16_35
Theory : co-recursion
Home
Index