Nuprl Lemma : mset_mon_for_elim
∀s:DSet. ∀T:Type. ∀f:T ⟶ (|s| List). ∀as:T List.
((For{mset_mon{s}} x ∈ as. mk_mset(f[x])) = mk_mset(For{<s List, @>} x ∈ as. f[x]) ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_mon: mset_mon{s},
mk_mset: mk_mset(as),
mset: MSet{s},
lapp_mon: <s List, @>,
mon_for: For{g} x ∈ as. f[x],
list: T List,
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
mset_mon: mset_mon{s},
grp_id: e,
pi2: snd(t),
pi1: fst(t),
lapp_mon: <s List, @>,
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
guard: {T},
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
subtype_rel: A ⊆r B,
grp_op: *,
infix_ap: x f y,
mk_mset: mk_mset(as),
null_mset: 0{s},
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
mset_sum: a + b
Lemmas referenced :
list_wf,
istype-universe,
set_car_wf,
dset_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
list-cases,
mon_for_nil_lemma,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
istype-false,
le_wf,
subtract-1-ge-0,
subtype_base_sq,
intformeq_wf,
int_formula_prop_eq_lemma,
set_subtype_base,
int_subtype_base,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
decidable__le,
mon_for_cons_lemma,
nat_wf,
mk_mset_wf,
nil_wf,
equal_wf,
squash_wf,
true_wf,
mset_sum_wf,
mset_wf,
append_wf,
mon_for_wf,
lapp_mon_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionIsType,
setElimination,
rename,
universeEquality,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityIsType1,
because_Cache,
dependent_set_memberEquality_alt,
instantiate,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
imageElimination,
equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
imageMemberEquality
Latex:
\mforall{}s:DSet. \mforall{}T:Type. \mforall{}f:T {}\mrightarrow{} (|s| List). \mforall{}as:T List.
((For\{mset\_mon\{s\}\} x \mmember{} as. mk\_mset(f[x])) = mk\_mset(For\{<s List, @>\} x \mmember{} as. f[x]))
Date html generated:
2019_10_16-PM-01_06_31
Last ObjectModification:
2018_10_08-PM-00_17_17
Theory : mset
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