Nuprl Lemma : comb_for_permr_wf
λT,as,bs,z. (as ≡(T) bs) ∈ T:Type ⟶ as:(T List) ⟶ bs:(T List) ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
list: T List,
prop: ℙ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
permr_wf,
squash_wf,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
isectElimination,
inhabitedIsType,
universeEquality
Latex:
\mlambda{}T,as,bs,z. (as \mequiv{}(T) bs) \mmember{} T:Type {}\mrightarrow{} as:(T List) {}\mrightarrow{} bs:(T List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2019_10_16-PM-01_00_18
Last ObjectModification:
2018_10_08-AM-10_18_07
Theory : perms_2
Home
Index