Nuprl Lemma : decidable__iseg
∀[T:Type]. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ (∀L1,L2:T List. Dec(L1 ≤ L2)))
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
decidable_functionality,
iseg_wf,
and_wf,
le_wf,
length_wf,
equal_wf,
list_wf,
firstn_wf,
iseg-iff-firstn,
decidable__and2,
decidable__le,
decidable__equal_list,
all_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
productElimination,
isect_memberEquality,
because_Cache,
sqequalRule,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}L1,L2:T List. Dec(L1 \mleq{} L2)))
Date html generated:
2016_05_14-PM-01_31_32
Last ObjectModification:
2015_12_26-PM-05_24_17
Theory : list_1
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