Nuprl Lemma : seq-count_wf
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. ∀[f:ℕ ⟶ T]. ∀[x:T]. ∀[j:ℕ]. (#{i<j|f i eq x} ∈ ℕj + 1)
Proof
Definitions occuring in Statement :
seq-count: #{i<j|f i eq x},
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
seq-count: #{i<j|f i eq x},
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
bool-size_wf,
compose_wf,
int_seg_wf,
bool_wf,
subtype_rel_dep_function,
nat_wf,
int_seg_subtype_nat,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
hypothesis,
cumulativity,
applyEquality,
lambdaEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. \mforall{}[x:T]. \mforall{}[j:\mBbbN{}]. (\#\{i<j|f i eq x\} \mmember{} \mBbbN{}j + 1)
Date html generated:
2016_05_15-PM-04_43_53
Last ObjectModification:
2015_12_27-PM-02_38_57
Theory : general
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