Nuprl Lemma : mset_prod_wf2
∀g:DMon. ∀a,b:FiniteSet{g↓set}. (a × b ∈ FiniteSet{g↓set})
Proof
Definitions occuring in Statement :
mset_prod: a × b,
finite_set: FiniteSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset_of_mon: g↓set,
dmon: DMon
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
finite_set: FiniteSet{s},
uall: ∀[x:A]. B[x],
dmon: DMon,
mon: Mon,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
mset_prod: a × b,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
infix_ap: x f y,
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
set_eq_wf,
b2i_bounds,
iff_weakening_equal,
mset_count_inj,
true_wf,
squash_wf,
mset_inj_wf,
grp_car_wf,
grp_op_wf,
infix_ap_wf,
mset_inj_wf_f,
mset_union_mon_wf,
mset_for_wf,
false_wf,
mset_count_bound_for_union,
dmon_wf,
finite_set_wf,
nat_wf,
dset_of_mon_wf,
mset_count_wf,
le_wf,
all_wf,
dset_of_mon_wf0,
set_car_wf,
mset_prod_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
natural_numberEquality,
because_Cache,
independent_pairFormation,
functionEquality,
independent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination
Latex:
\mforall{}g:DMon. \mforall{}a,b:FiniteSet\{g\mdownarrow{}set\}. (a \mtimes{} b \mmember{} FiniteSet\{g\mdownarrow{}set\})
Date html generated:
2016_05_16-AM-07_52_05
Last ObjectModification:
2016_01_16-PM-11_40_21
Theory : mset
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