Nuprl Lemma : seq-tl-len
∀[T:Type]. ∀[s:sequence(T)]. ||seq-tl(s)|| ~ ||s|| - 1 supposing 0 < ||s||
Proof
Definitions occuring in Statement :
seq-tl: seq-tl(s),
seq-len: ||s||,
sequence: sequence(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
guard: {T},
sq_type: SQType(T),
true: True,
less_than': less_than'(a;b),
top: Top,
subtype_rel: A ⊆r B,
subtract: n - m,
uiff: uiff(P;Q),
prop: ℙ,
false: False,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
and: P ∧ Q,
le: A ≤ B,
pi1: fst(t),
seq-tl: seq-tl(s),
seq-len: ||s||,
sequence: sequence(T),
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
sequence_wf,
seq-len_wf,
less_than_wf,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-le-2,
false_wf,
decidable__le,
subtract_wf,
int_subtype_base,
le_wf,
set_subtype_base,
nat_wf,
subtype_base_sq
Rules used in proof :
universeEquality,
sqequalAxiom,
equalitySymmetry,
equalityTransitivity,
minusEquality,
because_Cache,
voidEquality,
isect_memberEquality,
applyEquality,
addEquality,
independent_functionElimination,
voidElimination,
lambdaFormation,
independent_pairFormation,
unionElimination,
dependent_functionElimination,
dependent_set_memberEquality,
rename,
setElimination,
productElimination,
hypothesisEquality,
natural_numberEquality,
lambdaEquality,
intEquality,
sqequalRule,
independent_isectElimination,
hypothesis,
cumulativity,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. ||seq-tl(s)|| \msim{} ||s|| - 1 supposing 0 < ||s||
Date html generated:
2018_07_25-PM-01_29_15
Last ObjectModification:
2018_06_17-PM-10_09_26
Theory : arithmetic
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