Nuprl Lemma : compat-append
∀[T:Type]. ∀as,cs,bs,ds:T List. (as @ bs || cs @ ds ⇒ as || cs)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
compat: l1 || l2,
or: P ∨ Q,
guard: {T},
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
list_induction,
all_wf,
list_wf,
compat_wf,
append_wf,
nil_iseg,
iseg_wf,
nil_wf,
cons_wf,
list_ind_cons_lemma,
compat-cons
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
functionEquality,
independent_functionElimination,
rename,
because_Cache,
dependent_functionElimination,
universeEquality,
inlFormation,
inrFormation,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}as,cs,bs,ds:T List. (as @ bs || cs @ ds {}\mRightarrow{} as || cs)
Date html generated:
2016_05_15-PM-03_49_59
Last ObjectModification:
2015_12_27-PM-01_22_42
Theory : general
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