Nuprl Lemma : bdd-all-btrue
∀[n:ℕ]. (bdd-all(n;x.tt) ~ tt)
Proof
Definitions occuring in Statement :
bdd-all: bdd-all(n;i.P[i])
,
nat: ℕ
,
btrue: tt
,
uall: ∀[x:A]. B[x]
,
sqequal: s ~ t
Definitions unfolded in proof :
bdd-all: bdd-all(n;i.P[i])
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
nat: ℕ
,
implies: P
⇒ Q
,
false: False
,
ge: i ≥ j
,
guard: {T}
,
uimplies: b supposing a
,
prop: ℙ
,
all: ∀x:A. B[x]
,
top: Top
,
decidable: Dec(P)
,
or: P ∨ Q
,
iff: P
⇐⇒ Q
,
and: P ∧ Q
,
not: ¬A
,
rev_implies: P
⇐ Q
,
uiff: uiff(P;Q)
,
subtract: n - m
,
subtype_rel: A ⊆r B
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
true: True
,
band: p ∧b q
,
ifthenelse: if b then t else f fi
,
btrue: tt
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
sq_type: SQType(T)
,
bnot: ¬bb
,
assert: ↑b
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
primrec0_lemma,
istype-void,
decidable__le,
subtract_wf,
istype-false,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
primrec-unroll,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
Error :lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
axiomSqEquality,
Error :isect_memberEquality_alt,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
intEquality,
minusEquality,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
equalityElimination,
Error :dependent_pairFormation_alt,
Error :equalityIsType1,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. (bdd-all(n;x.tt) \msim{} tt)
Date html generated:
2019_06_20-PM-01_04_56
Last ObjectModification:
2019_06_20-PM-01_00_25
Theory : bool_1
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