Nuprl Lemma : guarded_permutation_transitivity
∀[T:Type]. ∀[P:L:(T List) ⟶ ℕ||L|| - 1 ⟶ ℙ]. Trans(T List)(_1 guarded_permutation(T;P) _2)
Proof
Definitions occuring in Statement :
guarded_permutation: guarded_permutation(T;P),
length: ||as||,
list: T List,
trans: Trans(T;x,y.E[x; y]),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
guarded_permutation: guarded_permutation(T;P),
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
false: False,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
subtract: n - m,
so_apply: x[s]
Lemmas referenced :
rel_star_transitivity,
exists_wf,
int_seg_wf,
subtract_wf,
length_wf,
equal_wf,
swap_wf,
decidable__lt,
subtract-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
false_wf,
lelt_wf,
add-member-int_seg2,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
infix_ap_wf,
list_wf,
rel_star_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
productEquality,
applyEquality,
functionExtensionality,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
dependent_functionElimination,
cumulativity,
unionElimination,
pointwiseFunctionality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_functionElimination,
instantiate,
universeEquality,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:L:(T List) {}\mrightarrow{} \mBbbN{}||L|| - 1 {}\mrightarrow{} \mBbbP{}]. Trans(T List)($_{1}$ guarded\_per\000Cmutation(T;P) $_{2}$)
Date html generated:
2017_10_01-AM-08_38_35
Last ObjectModification:
2017_07_26-PM-04_27_05
Theory : list!
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