Nuprl Lemma : iff_weakening_ext-eq
∀[A,B:Type]. {A ⇐⇒ B} supposing A ≡ B
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
ext-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
introduction,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
hypothesis,
rename,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
cumulativity,
universeEquality
Latex:
\mforall{}[A,B:Type]. \{A \mLeftarrow{}{}\mRightarrow{} B\} supposing A \mequiv{} B
Date html generated:
2016_10_21-AM-09_36_00
Last ObjectModification:
2016_08_06-PM-05_31_55
Theory : subtype_0
Home
Index