Nuprl Lemma : compat-iff-common-iseg
∀[T:Type]. ∀l1,l2:T List. (l1 || l2 ⇐⇒ ∃l:T List. (l1 ≤ l ∧ l2 ≤ l))
Proof
Definitions occuring in Statement :
compat: l1 || l2,
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
compat: l1 || l2,
or: P ∨ Q,
exists: ∃x:A. B[x],
cand: A c∧ B
Lemmas referenced :
compat_wf,
exists_wf,
list_wf,
and_wf,
iseg_wf,
iseg_weakening,
common_iseg_compat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
universeEquality,
unionElimination,
dependent_pairFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. (l1 || l2 \mLeftarrow{}{}\mRightarrow{} \mexists{}l:T List. (l1 \mleq{} l \mwedge{} l2 \mleq{} l))
Date html generated:
2016_05_15-PM-03_46_12
Last ObjectModification:
2015_12_27-PM-01_20_46
Theory : general
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