Nuprl Lemma : sq_or_squash
∀[a,b:ℙ]. uiff((↓a) ↓∨ (↓b);a ↓∨ b)
Proof
Definitions occuring in Statement :
sq_or: a ↓∨ b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T
Definitions unfolded in proof :
sq_or: a ↓∨ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
or: P ∨ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
or_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
imageElimination,
unionElimination,
thin,
inlFormation,
hypothesis,
hypothesisEquality,
imageMemberEquality,
baseClosed,
inrFormation,
lemma_by_obid,
isectElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[a,b:\mBbbP{}]. uiff((\mdownarrow{}a) \mdownarrow{}\mvee{} (\mdownarrow{}b);a \mdownarrow{}\mvee{} b)
Date html generated:
2016_05_13-PM-03_13_41
Last ObjectModification:
2016_01_06-PM-05_49_46
Theory : core_2
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