Nuprl Lemma : l_subset_right_cons_trivial
∀[T:Type]. ∀x:T. ∀L:T List. l_subset(T;L;[x / L])
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
l_subset: l_subset(T;as;bs),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
cons_member,
equal_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
hypothesis,
inrFormation,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}L:T List. l\_subset(T;L;[x / L])
Date html generated:
2016_05_14-AM-07_53_57
Last ObjectModification:
2015_12_26-PM-04_48_01
Theory : list_1
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