Nuprl Lemma : comb_for_l_all_wf
λT,L,P,z. (∀x∈L.P[x]) ∈ T:Type ⟶ L:(T List) ⟶ P:(T ⟶ ℙ) ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
list: T List,
prop: ℙ,
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,
uall: ∀[x:A]. B[x],
subtype: S ⊆ T,
suptype: suptype(S; T),
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
l_all_wf,
set_wf,
l_member_wf,
squash_wf,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
setElimination,
rename,
because_Cache,
sqequalRule,
hypothesis,
functionExtensionality,
universeEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity
Latex:
\mlambda{}T,L,P,z. (\mforall{}x\mmember{}L.P[x]) \mmember{} T:Type {}\mrightarrow{} L:(T List) {}\mrightarrow{} P:(T {}\mrightarrow{} \mBbbP{}) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2016_05_14-AM-07_47_46
Last ObjectModification:
2015_12_26-PM-02_55_04
Theory : list_1
Home
Index