Nuprl Lemma : permutation_transitivity
∀[A:Type]. ∀as,bs,cs:A List. (permutation(A;as;bs) ⇒ permutation(A;bs;cs) ⇒ permutation(A;as;cs))
Proof
Definitions occuring in Statement :
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 :
permutation: permutation(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
cand: A c∧ B,
compose: f o g,
inject: Inj(A;B;f),
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T},
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b
Lemmas referenced :
permute_list_length,
equal_wf,
length_wf,
list_wf,
compose_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype,
false_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
subtype_rel_self,
int_seg_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
squash_wf,
true_wf,
permute_permute_list,
permute_list_wf,
iff_weakening_equal,
inject_wf,
exists_wf,
and_wf,
le_wf,
subtype_rel_weakening,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
intEquality,
cumulativity,
promote_hyp,
dependent_set_memberEquality,
equalityTransitivity,
dependent_pairFormation,
natural_numberEquality,
applyEquality,
lambdaEquality,
independent_isectElimination,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
int_eqEquality,
computeAll,
functionExtensionality,
setElimination,
rename,
imageElimination,
equalityUniverse,
levelHypothesis,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
productEquality,
functionEquality,
instantiate
Latex:
\mforall{}[A:Type]. \mforall{}as,bs,cs:A List. (permutation(A;as;bs) {}\mRightarrow{} permutation(A;bs;cs) {}\mRightarrow{} permutation(A;as;cs))
Date html generated:
2017_04_17-AM-08_11_11
Last ObjectModification:
2017_02_27-PM-04_38_18
Theory : list_1
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