Nuprl Lemma : iseg-l_contains
∀[T:Type]. ∀x,y:T List. (x ≤ y ⇒ x ⊆ y)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
l_contains: A ⊆ B,
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],
l_contains: A ⊆ B,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iseg_member,
l_member_wf,
iseg_wf,
l_all_iff,
all_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
addLevel,
because_Cache,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x,y:T List. (x \mleq{} y {}\mRightarrow{} x \msubseteq{} y)
Date html generated:
2019_06_20-PM-01_29_56
Last ObjectModification:
2018_08_24-PM-11_19_47
Theory : list_1
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