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: `ℙ` guard: `{T}` implies: `P `` Q` and: `P ∧ Q`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` implies: `P `` Q` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` prop: `ℙ` 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

Home Index