Nuprl Lemma : decidable__dset_eq
∀s:DSet. ∀a,b:|s|. Dec(a = b ∈ |s|)
Proof
Definitions occuring in Statement :
dset: DSet,
set_car: |p|,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
infix_ap: x f y,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable_functionality,
equal_wf,
set_car_wf,
assert_wf,
set_eq_wf,
iff_weakening_uiff,
assert_of_dset_eq,
decidable__assert,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_pairFormation,
dependent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:|s|. Dec(a = b)
Date html generated:
2016_05_15-PM-00_04_03
Last ObjectModification:
2015_12_26-PM-11_28_51
Theory : sets_1
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