Nuprl Lemma : sub-mset_weakening
∀[T:Type]. ∀L1,L2:T List. (permutation(T;L1;L2) ⇒ sub-mset(T; L1; L2))
Proof
Definitions occuring in Statement :
sub-mset: sub-mset(T; L1; L2),
permutation: permutation(T;L1;L2),
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,
sub-mset: sub-mset(T; L1; L2),
exists: ∃x:A. B[x],
member: t ∈ T,
top: Top,
prop: ℙ
Lemmas referenced :
nil_wf,
nil-append,
permutation_wf,
append_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (permutation(T;L1;L2) {}\mRightarrow{} sub-mset(T; L1; L2))
Date html generated:
2016_05_15-PM-04_32_02
Last ObjectModification:
2015_12_27-PM-02_48_48
Theory : general
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