Nuprl Lemma : set_prod_wf
∀[s,t:DSet]. (s × t ∈ DSet)
Proof
Definitions occuring in Statement :
set_prod: s × t,
dset: DSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
set_prod: s × t,
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
uimplies: b supposing a,
eqfun_p: IsEqFun(T;eq),
infix_ap: x f y,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
mk_dset_wf,
set_car_wf,
eq_pair_wf,
dset_wf,
assert_of_eq_pair,
assert_wf,
assert_witness,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
productElimination,
independent_pairEquality,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
independent_functionElimination
Latex:
\mforall{}[s,t:DSet]. (s \mtimes{} t \mmember{} DSet)
Date html generated:
2016_05_15-PM-00_05_47
Last ObjectModification:
2015_12_26-PM-11_27_38
Theory : sets_1
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