Nuprl Lemma : respects-equality-bag
∀[A,B:Type]. respects-equality(bag(A);bag(B)) supposing respects-equality(A;B)
Proof
Definitions occuring in Statement :
bag: bag(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,
bag: bag(T),
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
respects-equality: respects-equality(S;T),
label: ...$L... t,
guard: {T},
surject: Surj(A;B;f),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
permute_list: (L o f)
Lemmas referenced :
respects-equality-quotient,
list_wf,
permutation_wf,
permutation-equiv,
respects-equality-list,
respects-equality_wf,
istype-universe,
permutation_inversion,
change-equality-type,
inject_wf,
int_seg_wf,
length_wf,
permute_list_wf,
respects-equality-list-type,
injection-is-surjection,
length_wf_nat,
int_seg_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
set_subtype_base,
lelt_wf,
int_subtype_base,
subtype_base_sq,
select_wf,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
permutation-length,
equal_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
select-mklist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality_alt,
inhabitedIsType,
universeIsType,
because_Cache,
independent_isectElimination,
lambdaFormation_alt,
instantiate,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
independent_pairFormation,
productIsType,
natural_numberEquality,
equalityIstype,
applyLambdaEquality,
setElimination,
rename,
unionElimination,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
applyEquality,
intEquality,
closedConclusion,
sqequalBase,
cumulativity,
dependent_set_memberEquality_alt,
imageElimination,
imageMemberEquality,
baseClosed,
functionExtensionality
Latex:
\mforall{}[A,B:Type]. respects-equality(bag(A);bag(B)) supposing respects-equality(A;B)
Date html generated:
2019_10_15-AM-10_59_48
Last ObjectModification:
2018_11_29-PM-07_12_40
Theory : bags
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