Nuprl Lemma : set_eq_wf
∀[p:PosetSig]. (=b ∈ |p| ⟶ |p| ⟶ 𝔹)
Proof
Definitions occuring in Statement :
set_eq: =b,
set_car: |p|,
poset_sig: PosetSig,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poset_sig: PosetSig,
set_eq: =b,
set_car: |p|,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid
Latex:
\mforall{}[p:PosetSig]. (=\msubb{} \mmember{} |p| {}\mrightarrow{} |p| {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_15-PM-00_03_53
Last ObjectModification:
2015_12_26-PM-11_28_53
Theory : sets_1
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