Nuprl Lemma : permutation-subtype
∀[A,B:Type]. ∀[L1,L2:A List]. (permutation(A;L1;L2) ⇒ (A ⊆r B) ⇒ permutation(B;L1;L2))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
list: T List,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_list,
equal_functionality_wrt_subtype_rel2,
list_wf,
inject_wf,
int_seg_wf,
length_wf,
equal_wf,
permute_list_wf,
subtype_rel_wf,
permutation_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
hypothesis,
independent_pairFormation,
introduction,
extract_by_obid,
isectElimination,
independent_isectElimination,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productEquality,
natural_numberEquality,
because_Cache,
functionExtensionality,
applyEquality,
sqequalRule,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L1,L2:A List]. (permutation(A;L1;L2) {}\mRightarrow{} (A \msubseteq{}r B) {}\mRightarrow{} permutation(B;L1;L2))
Date html generated:
2017_04_17-AM-08_10_23
Last ObjectModification:
2017_02_27-PM-04_37_35
Theory : list_1
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