Nuprl Lemma : eq_pair_wf
∀[s,t:DSet]. ∀[a,b:|s| × |t|]. (a =b b ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq_pair: a =b b,
dset: DSet,
set_car: |p|,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
eq_pair: a =b b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
pi1: fst(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
pi2: snd(t),
bfalse: ff,
infix_ap: x f y,
prop: ℙ
Lemmas referenced :
infix_ap_wf,
set_car_wf,
bool_wf,
set_eq_wf,
eqtt_to_assert,
assert_of_dset_eq,
equal_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
productElimination,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
productEquality,
isect_memberEquality
Latex:
\mforall{}[s,t:DSet]. \mforall{}[a,b:|s| \mtimes{} |t|]. (a =\msubb{} b \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_13_15
Last ObjectModification:
2017_02_28-PM-01_57_23
Theory : sets_1
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