Nuprl Lemma : null-upto
∀[n:ℕ]. (null(upto(n)) ~ (n =z 0))
Proof
Definitions occuring in Statement :
upto: upto(n),
null: null(as),
nat: ℕ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
top: Top,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x]
Lemmas referenced :
upto_is_nil,
subtype_base_sq,
bool_wf,
bool_subtype_base,
equal_wf,
squash_wf,
true_wf,
null-length-zero,
upto_wf,
subtype_rel_list,
int_seg_wf,
top_wf,
eq_int_wf,
iff_weakening_equal,
length_upto,
nat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
dependent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[n:\mBbbN{}]. (null(upto(n)) \msim{} (n =\msubz{} 0))
Date html generated:
2017_04_17-AM-07_57_15
Last ObjectModification:
2017_02_27-PM-04_27_48
Theory : list_1
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