Nuprl Lemma : strong-subtype-eq3
∀[A,B:Type]. ∀[b:B]. ∀[a:A]. {b = a ∈ A supposing b = a ∈ B} supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T}
Lemmas referenced :
strong-subtype-eq2
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[A,B:Type]. \mforall{}[b:B]. \mforall{}[a:A]. \{b = a supposing b = a\} supposing strong-subtype(A;B)
Date html generated:
2016_05_13-PM-04_11_35
Last ObjectModification:
2015_12_26-AM-11_12_26
Theory : subtype_1
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