Nuprl Lemma : uequiv_rel_iff
UniformEquivRel(ℙ;A,B.A ⇐⇒ B)
Proof
Definitions occuring in Statement :
uequiv_rel: UniformEquivRel(T;x,y.E[x; y]),
prop: ℙ,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
uequiv_rel: UniformEquivRel(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
Error :isect_memberFormation_alt,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
because_Cache,
Error :universeIsType,
universeEquality,
sqequalHypSubstitution,
productElimination,
thin,
independent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType
Latex:
UniformEquivRel(\mBbbP{};A,B.A \mLeftarrow{}{}\mRightarrow{} B)
Date html generated:
2019_06_20-PM-00_29_03
Last ObjectModification:
2018_09_26-AM-11_56_04
Theory : rel_1
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