Nuprl Lemma : ring-as-list_wf
∀[T:Type]. ∀[L:T List]. ∀[f:{i:T| (i ∈ L)} ⟶ {i:T| (i ∈ L)} ]. (ring-as-list(T;L;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
ring-as-list: ring-as-list(T;L;f),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ring-as-list: ring-as-list(T;L;f),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
inject_wf,
l_member_wf,
all_wf,
exists_wf,
nat_wf,
equal_wf,
fun_exp_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
dependent_set_memberEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:\{i:T| (i \mmember{} L)\} {}\mrightarrow{} \{i:T| (i \mmember{} L)\} ]. (ring-as-list(T;L;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-06_20_57
Last ObjectModification:
2015_12_27-PM-00_05_36
Theory : general
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