Nuprl Lemma : comb_for_cons_wf_listp
λA,l,x,z. [x / l] ∈ A:Type ⟶ l:(A List) ⟶ x:A ⟶ (↓True) ⟶ A List+
Proof
Definitions occuring in Statement :
listp: A List+,
cons: [a / b],
list: T List,
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,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
cons_wf_listp,
squash_wf,
true_wf,
istype-universe,
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,
universeEquality
Latex:
\mlambda{}A,l,x,z. [x / l] \mmember{} A:Type {}\mrightarrow{} l:(A List) {}\mrightarrow{} x:A {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} A List\msupplus{}
Date html generated:
2019_10_15-AM-10_53_30
Last ObjectModification:
2018_10_09-AM-10_31_06
Theory : list!
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