Nuprl Lemma : squash_equal
∀[T:Type]. ∀[x,y:T]. uiff(↓x = y ∈ T;x = y ∈ T)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
squash: ↓T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ
Lemmas referenced :
equal_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
imageElimination,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T]. uiff(\mdownarrow{}x = y;x = y)
Date html generated:
2016_05_13-PM-03_14_04
Last ObjectModification:
2016_01_06-PM-05_49_55
Theory : core_2
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