Nuprl Lemma : union_functionality_wrt_uiff

`∀[P1,P2,Q1,Q2:ℙ].  ({uiff(P1;P2)} `` {uiff(Q1;Q2)} `` {P1 + Q1 `⇐⇒` P2 + Q2})`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` iff: `P `⇐⇒` Q` implies: `P `` Q` union: `left + right`
Definitions unfolded in proof :  guard: `{T}` or: `P ∨ Q` uall: `∀[x:A]. B[x]` implies: `P `` Q` uiff: `uiff(P;Q)` and: `P ∧ Q` iff: `P `⇐⇒` Q` uimplies: `b supposing a` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q`
Lemmas referenced :  or_wf uiff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  lambdaFormation sqequalHypSubstitution productElimination thin independent_pairFormation unionElimination inlFormation independent_isectElimination hypothesis hypothesisEquality inrFormation cut introduction extract_by_obid isectElimination Error :inhabitedIsType,  Error :universeIsType,  universeEquality

Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}].    (\{uiff(P1;P2)\}  {}\mRightarrow{}  \{uiff(Q1;Q2)\}  {}\mRightarrow{}  \{P1  +  Q1  \mLeftarrow{}{}\mRightarrow{}  P2  +  Q2\})

Date html generated: 2019_06_20-AM-11_17_22
Last ObjectModification: 2018_09_26-AM-10_24_50

Theory : core_2

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