Nuprl Lemma : isaxiom-bool-if-bunion-unit-prod
∀[t:Unit ⋃ (Top × Top)]. (isaxiom(t) ∈ 𝔹)
Proof
Definitions occuring in Statement :
b-union: A ⋃ B,
bfalse: ff,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
isaxiom: if z = Ax then a otherwise b,
unit: Unit,
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
isaxiom_wf_listunion,
top_wf,
b-union_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality
Latex:
\mforall{}[t:Unit \mcup{} (Top \mtimes{} Top)]. (isaxiom(t) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-10_09_35
Last ObjectModification:
2015_12_27-PM-05_59_17
Theory : eval!all
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