Nuprl Lemma : compat-iseg
∀[T:Type]. ∀L1,L2,L3:T List. (L1 ≤ L2 ⇒ L2 || L3 ⇒ L1 || L3)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
compat-append,
nil_wf,
append_nil_sq,
subtype_rel_list,
top_wf,
compat_wf,
exists_wf,
list_wf,
equal_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
cumulativity,
hypothesis,
independent_functionElimination,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2,L3:T List. (L1 \mleq{} L2 {}\mRightarrow{} L2 || L3 {}\mRightarrow{} L1 || L3)
Date html generated:
2016_10_25-AM-10_48_22
Last ObjectModification:
2016_07_12-AM-06_57_34
Theory : general
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