Nuprl Lemma : fseg-iseg-reverse
∀[T:Type]. ∀[L1,L2:T List]. (fseg(T;L1;L2) ⇐⇒ rev(L1) ≤ rev(L2))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
iseg: l1 ≤ l2,
reverse: rev(as),
list: T List,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
top: Top
Lemmas referenced :
exists_wf,
list_wf,
equal_wf,
append_wf,
reverse_wf,
length_wf_nat,
nat_wf,
squash_wf,
true_wf,
reverse_append,
iff_weakening_equal,
reverse-reverse,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
universeEquality,
dependent_set_memberEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
equalityUniverse,
levelHypothesis,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
dependent_pairFormation,
hyp_replacement,
applyLambdaEquality,
setElimination,
rename,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. (fseg(T;L1;L2) \mLeftarrow{}{}\mRightarrow{} rev(L1) \mleq{} rev(L2))
Date html generated:
2017_04_17-AM-08_42_27
Last ObjectModification:
2017_02_27-PM-05_02_14
Theory : list_1
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