Nuprl Lemma : equiv_rel_iff
EquivRel(ℙ;A,B.A ⇐⇒ B)
Proof
Definitions occuring in Statement :
equiv_rel: EquivRel(T;x,y.E[x; y]),
prop: ℙ,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
prop: ℙ,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :universeIsType,
sqequalHypSubstitution,
hypothesisEquality,
universeEquality,
cut,
hypothesis,
productElimination,
thin,
independent_functionElimination,
because_Cache,
sqequalRule,
Error :productIsType,
Error :functionIsType,
Error :inhabitedIsType,
independent_pairFormation,
Error :lambdaFormation_alt
Latex:
EquivRel(\mBbbP{};A,B.A \mLeftarrow{}{}\mRightarrow{} B)
Date html generated:
2019_06_20-PM-00_29_01
Last ObjectModification:
2018_09_29-PM-11_16_38
Theory : rel_1
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