Nuprl Lemma : append_iseg
∀[T:Type]. ∀as,bs,cs:T List. (as @ bs ≤ as @ cs ⇐⇒ bs ≤ cs)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀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 :
equal_wf,
list_wf,
append_wf,
exists_wf,
squash_wf,
true_wf,
iff_weakening_equal,
append_assoc,
length_wf,
append-cancellation
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
lambdaEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
equalityUniverse,
levelHypothesis,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs,cs:T List. (as @ bs \mleq{} as @ cs \mLeftarrow{}{}\mRightarrow{} bs \mleq{} cs)
Date html generated:
2017_04_17-AM-08_45_32
Last ObjectModification:
2017_02_27-PM-05_04_16
Theory : list_1
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