Nuprl Lemma : b-exists-bfalse
∀[n:ℕ]. ((∃x<n.ff)_b ~ ff)
Proof
Definitions occuring in Statement :
b-exists: (∃i<n.P[i])_b,
nat: ℕ,
bfalse: ff,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
b-exists: (∃i<n.P[i])_b,
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,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
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{}]. ((\mexists{}x<n.ff)\_b \msim{} ff)
Date html generated:
2019_06_20-PM-01_04_53
Last ObjectModification:
2019_06_20-PM-01_00_37
Theory : bool_1
Home
Index