Nuprl Lemma : ext-eq_transitivity
∀[A,B,C:Type]. (A ≡ C) supposing (B ≡ C and A ≡ B)
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
and_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lambdaEquality,
hypothesisEquality,
applyEquality,
hypothesis,
independent_pairFormation,
independent_pairEquality,
axiomEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. (A \mequiv{} C) supposing (B \mequiv{} C and A \mequiv{} B)
Date html generated:
2016_05_13-PM-03_19_07
Last ObjectModification:
2015_12_26-AM-09_07_56
Theory : subtype_0
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