Nuprl Lemma : l_all_reverse
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀L:T List. ((∀x∈rev(L).P[x]) ⇐⇒ (∀x∈L.P[x]))
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
reverse: rev(as),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
l_all_iff,
reverse_wf,
l_member_wf,
l_all_wf,
list_wf,
member-reverse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
productElimination,
independent_functionElimination,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}L:T List. ((\mforall{}x\mmember{}rev(L).P[x]) \mLeftarrow{}{}\mRightarrow{} (\mforall{}x\mmember{}L.P[x]))
Date html generated:
2016_05_14-AM-06_41_49
Last ObjectModification:
2015_12_26-PM-00_29_48
Theory : list_0
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