Nuprl Lemma : comb_for_listify_wf
λT,m,n,f,z. listify(f;m;n) ∈ T:Type ⟶ m:ℤ ⟶ n:ℤ ⟶ f:({m..n-} ⟶ T) ⟶ (↓True) ⟶ (T List)
Proof
Definitions occuring in Statement :
listify: listify(f;m;n),
list: T List,
int_seg: {i..j-},
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
listify_wf,
squash_wf,
true_wf,
int_seg_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :functionIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mlambda{}T,m,n,f,z. listify(f;m;n) \mmember{} T:Type {}\mrightarrow{} m:\mBbbZ{} {}\mrightarrow{} n:\mBbbZ{} {}\mrightarrow{} f:(\{m..n\msupminus{}\} {}\mrightarrow{} T) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} (T List)
Date html generated:
2019_06_20-PM-00_38_28
Last ObjectModification:
2018_10_02-PM-05_40_42
Theory : list_0
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