Nuprl Lemma : comb_for_ball_wf
λA,as,f,z. ∀bx(:A) ∈ as. f[x] ∈ A:Type ⟶ as:(A List) ⟶ f:(A ⟶ 𝔹) ⟶ (↓True) ⟶ 𝔹
Proof
Definitions occuring in Statement :
ball: ball,
list: T List,
bool: 𝔹,
so_apply: x[s],
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 :
ball_wf,
squash_wf,
true_wf,
istype-universe,
bool_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,
functionIsType,
universeEquality
Latex:
\mlambda{}A,as,f,z. \mforall{}\msubb{}x(:A) \mmember{} as. f[x] \mmember{} A:Type {}\mrightarrow{} as:(A List) {}\mrightarrow{} f:(A {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbB{}
Date html generated:
2019_10_16-PM-01_02_51
Last ObjectModification:
2018_10_08-AM-11_23_28
Theory : list_2
Home
Index