Nuprl Lemma : permutation_weakening
∀[A:Type]. ∀as,bs:A List. permutation(A;as;bs) supposing as = bs ∈ (A List)
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
int_seg_wf,
length_wf,
identity-injection,
equal_wf,
squash_wf,
true_wf,
list_wf,
permute_list_wf,
iff_weakening_equal,
permute_list-identity,
inject_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
dependent_pairFormation,
lambdaEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
cumulativity,
independent_pairFormation,
equalitySymmetry,
applyEquality,
imageElimination,
equalityTransitivity,
because_Cache,
functionEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
productEquality,
functionExtensionality
Latex:
\mforall{}[A:Type]. \mforall{}as,bs:A List. permutation(A;as;bs) supposing as = bs
Date html generated:
2017_04_17-AM-08_10_58
Last ObjectModification:
2017_02_27-PM-04_37_21
Theory : list_1
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