Nuprl Lemma : agree_on_equiv
∀[T:Type]. ∀[P:T ⟶ ℙ]. EquivRel(T List)(_1 agree_on(T;a.P[a]) _2)
Proof
Definitions occuring in Statement :
agree_on: agree_on(T;x.P[x]),
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
agree_on: agree_on(T;x.P[x]),
refl: Refl(T;x,y.E[x; y]),
infix_ap: x f y,
all: ∀x:A. B[x],
member: t ∈ T,
cand: A c∧ B,
implies: P ⇒ Q,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
so_apply: x[s],
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
so_lambda: λ2x.t[x],
le: A ≤ B,
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
length_wf,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
or_wf,
int_seg_wf,
list_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
equal_wf,
all_wf,
lelt_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
sqequalRule,
lambdaFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
applyEquality,
functionExtensionality,
independent_pairEquality,
axiomEquality,
addLevel,
levelHypothesis,
productEquality,
functionEquality,
universeEquality,
dependent_set_memberEquality,
independent_functionElimination,
inrFormation,
inlFormation,
imageElimination,
imageMemberEquality,
baseClosed,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. EquivRel(T List)($_{1}$ agree\_on(T;a.P[a]) $_\mbackslash{}f\000Cf7b2}$)
Date html generated:
2017_10_01-AM-08_38_59
Last ObjectModification:
2017_07_26-PM-04_27_20
Theory : list!
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