Nuprl Lemma : respects-equality-fset
∀[A,B:Type]. respects-equality(fset(A);fset(B)) supposing respects-equality(A;B)
Proof
Definitions occuring in Statement :
fset: fset(T),
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
fset: fset(T),
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
respects-equality: respects-equality(S;T),
prop: ℙ,
set-equal: set-equal(T;x;y),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_member: (x ∈ l),
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
respects-equality-quotient,
list_wf,
set-equal_wf,
set-equal-equiv,
respects-equality-list,
respects-equality_wf,
istype-universe,
respects-equality-list-type,
int_seg_wf,
length_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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,
select_member,
nat_properties,
change-equality-type,
l_member_wf,
istype-le,
istype-less_than
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
Error :universeIsType,
independent_isectElimination,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :equalityIstype,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
instantiate,
universeEquality,
natural_numberEquality,
setElimination,
rename,
productElimination,
unionElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
imageElimination,
equalitySymmetry,
equalityTransitivity,
Error :dependent_set_memberEquality_alt,
Error :productIsType
Latex:
\mforall{}[A,B:Type]. respects-equality(fset(A);fset(B)) supposing respects-equality(A;B)
Date html generated:
2019_06_20-PM-01_58_34
Last ObjectModification:
2018_12_19-PM-05_04_04
Theory : finite!sets
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