Nuprl Lemma : mset_prod_wf
∀g:DMon. ∀a,b:MSet{g↓set}. (a × b ∈ MSet{g↓set})
Proof
Definitions occuring in Statement :
mset_prod: a × b,
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset_of_mon: g↓set,
dmon: DMon
Definitions unfolded in proof :
mset_prod: a × b,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
dmon: DMon,
mon: Mon,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
so_apply: x[s]
Lemmas referenced :
mset_for_wf,
dset_of_mon_wf,
mset_union_mon_wf,
mset_inj_wf_f,
infix_ap_wf,
set_car_wf,
dset_of_mon_wf0,
grp_op_wf,
grp_car_wf,
mset_wf,
dmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
lambdaEquality,
setElimination,
rename,
functionEquality
Latex:
\mforall{}g:DMon. \mforall{}a,b:MSet\{g\mdownarrow{}set\}. (a \mtimes{} b \mmember{} MSet\{g\mdownarrow{}set\})
Date html generated:
2016_05_16-AM-07_52_01
Last ObjectModification:
2015_12_28-PM-05_59_57
Theory : mset
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