Nuprl Lemma : seq-adjoin_wf
∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T]. ∀[t:T]. (s++t ∈ ℕn + 1 ⟶ T)
Proof
Definitions occuring in Statement :
seq-adjoin: s++t,
int_seg: {i..j-},
nat: ℕ,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
seq-adjoin: s++t,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
seq-append_wf,
false_wf,
le_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
setElimination,
rename,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} T]. \mforall{}[t:T]. (s++t \mmember{} \mBbbN{}n + 1 {}\mrightarrow{} T)
Date html generated:
2016_05_13-PM-03_49_16
Last ObjectModification:
2015_12_26-AM-10_17_53
Theory : bar-induction
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