Nuprl Lemma : comb_for_swap_wf
λT,L,i,j,z. swap(L;i;j) ∈ T:Type ⟶ L:(T List) ⟶ i:ℕ||L|| ⟶ j:ℕ||L|| ⟶ (↓True) ⟶ (T List)
Proof
Definitions occuring in Statement :
swap: swap(L;i;j),
length: ||as||,
list: T List,
int_seg: {i..j-},
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
swap_wf,
squash_wf,
true_wf,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
inhabitedIsType,
natural_numberEquality,
universeEquality
Latex:
\mlambda{}T,L,i,j,z. swap(L;i;j) \mmember{} T:Type {}\mrightarrow{} L:(T List) {}\mrightarrow{} i:\mBbbN{}||L|| {}\mrightarrow{} j:\mBbbN{}||L|| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} (T List)
Date html generated:
2019_10_15-AM-10_58_07
Last ObjectModification:
2018_10_09-AM-09_57_47
Theory : list!
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