### 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

Home Index