Nuprl Lemma : sq_or_sq_or
∀[a,b,c:ℙ]. ({uiff(a ↓∨ b ↓∨ c;a ↓∨ (b ∨ c))} ∧ {uiff((b ↓∨ c) ↓∨ a;(b ∨ c) ↓∨ a)})
Proof
Definitions occuring in Statement :
sq_or: a ↓∨ b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
sq_or: a ↓∨ b,
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
uimplies: b supposing a,
squash: ↓T,
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
squash_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
imageElimination,
unionElimination,
thin,
inlFormation,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
imageMemberEquality,
baseClosed,
inrFormation,
because_Cache,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[a,b,c:\mBbbP{}]. (\{uiff(a \mdownarrow{}\mvee{} b \mdownarrow{}\mvee{} c;a \mdownarrow{}\mvee{} (b \mvee{} c))\} \mwedge{} \{uiff((b \mdownarrow{}\mvee{} c) \mdownarrow{}\mvee{} a;(b \mvee{} c) \mdownarrow{}\mvee{} a)\})
Date html generated:
2016_05_13-PM-03_13_24
Last ObjectModification:
2016_01_06-PM-05_48_22
Theory : core_2
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