Nuprl Lemma : dset_eq_refl
∀[s:DSet]. ∀[a:|s|]. a (=b) a = tt
Proof
Definitions occuring in Statement :
dset: DSet,
set_eq: =b,
set_car: |p|,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
infix_ap: x f y,
dset: DSet,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
eqtt_to_assert,
set_eq_wf,
set_car_wf,
dset_wf,
assert_of_dset_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[s:DSet]. \mforall{}[a:|s|]. a (=\msubb{}) a = tt
Date html generated:
2016_05_15-PM-00_04_05
Last ObjectModification:
2015_12_26-PM-11_28_35
Theory : sets_1
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