Nuprl Lemma : and_functionality_wrt_uiff

[P1,P2,Q1,Q2:ℙ].  ({uiff(P1;P2)}  {uiff(Q1;Q2)}  {uiff(P1 ∧ Q1;P2 ∧ Q2)})


Proof




Definitions occuring in Statement :  uiff: uiff(P;Q) uall: [x:A]. B[x] prop: guard: {T} implies:  Q and: P ∧ Q
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] implies:  Q uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a prop: member: t ∈ T
Lemmas referenced :  uiff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  lambdaFormation sqequalHypSubstitution productElimination thin independent_pairFormation cut hypothesis independent_isectElimination Error :productIsType,  Error :universeIsType,  hypothesisEquality introduction extract_by_obid isectElimination Error :inhabitedIsType,  universeEquality

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



Date html generated: 2019_06_20-AM-11_14_16
Last ObjectModification: 2018_09_26-AM-10_41_51

Theory : core_2


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