Nuprl Lemma : l_subset_cons_same
∀[T:Type]. ∀x:T. ∀L1,L2:T List. (l_subset(T;L1;L2) ⇒ l_subset(T;[x / L1];[x / L2]))
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],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
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,
cand: A c∧ B,
or: P ∨ Q,
prop: ℙ,
l_subset: l_subset(T;as;bs),
guard: {T}
Lemmas referenced :
l_subset_cons,
cons_wf,
cons_member,
l_member_wf,
l_subset_wf,
list_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
inlFormation,
independent_pairFormation,
universeEquality,
sqequalRule,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}L1,L2:T List. (l\_subset(T;L1;L2) {}\mRightarrow{} l\_subset(T;[x / L1];[x / L2]))
Date html generated:
2016_05_14-AM-07_54_25
Last ObjectModification:
2015_12_26-PM-04_48_50
Theory : list_1
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