Nuprl Lemma : list-decomp-nat-iseg
∀[T:Type]. ∀L:T List. ∀i:ℕ||L|| + 1. ∃K:T List. (K ≤ L ∧ (||K|| = i ∈ ℤ))
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
iseg: l1 ≤ l2,
prop: ℙ,
int_seg: {i..j-}
Lemmas referenced :
list-decomp-nat,
equal_wf,
list_wf,
append_wf,
and_wf,
iseg_wf,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
dependent_pairFormation,
hypothesis,
independent_pairFormation,
intEquality,
setElimination,
rename,
natural_numberEquality,
addEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}i:\mBbbN{}||L|| + 1. \mexists{}K:T List. (K \mleq{} L \mwedge{} (||K|| = i))
Date html generated:
2016_05_14-PM-03_01_15
Last ObjectModification:
2015_12_26-PM-01_56_41
Theory : list_1
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