Nuprl Lemma : comb_for_reduce2_wf
λA,T,L,k,i,f,z. reduce2(f;k;i;L) ∈ A:Type ⟶ T:Type ⟶ L:(T List) ⟶ k:A ⟶ i:ℕ ⟶ f:(T ⟶ {i..i + ||L||-} ⟶ A ⟶ A) ⟶\000C (↓True) ⟶ A
Proof
Definitions occuring in Statement :
reduce2: reduce2(f;k;i;as),
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
add: n + m,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ
Lemmas referenced :
reduce2_wf,
squash_wf,
true_wf,
istype-universe,
int_seg_wf,
length_wf,
nat_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,
functionIsType,
setElimination,
rename,
addEquality,
because_Cache,
inhabitedIsType,
universeEquality
Latex:
\mlambda{}A,T,L,k,i,f,z. reduce2(f;k;i;L) \mmember{} A:Type
{}\mrightarrow{} T:Type
{}\mrightarrow{} L:(T List)
{}\mrightarrow{} k:A
{}\mrightarrow{} i:\mBbbN{}
{}\mrightarrow{} f:(T {}\mrightarrow{} \{i..i + ||L||\msupminus{}\} {}\mrightarrow{} A {}\mrightarrow{} A)
{}\mrightarrow{} (\mdownarrow{}True)
{}\mrightarrow{} A
Date html generated:
2019_10_15-AM-10_54_55
Last ObjectModification:
2018_10_09-AM-10_21_31
Theory : list!
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