### Nuprl Lemma : and_functionality_wrt_rev_uimplies

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

Proof

Definitions occuring in Statement :  rev_uimplies: `rev_uimplies(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` rev_uimplies: `rev_uimplies(P;Q)` uimplies: `b supposing a` and: `P ∧ Q` cand: `A c∧ B` prop: `ℙ` member: `t ∈ T`
Lemmas referenced :  rev_uimplies_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  lambdaFormation cut sqequalHypSubstitution hypothesis independent_isectElimination thin productElimination independent_pairFormation Error :productIsType,  Error :universeIsType,  hypothesisEquality introduction extract_by_obid isectElimination Error :inhabitedIsType,  universeEquality

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

Date html generated: 2019_06_20-AM-11_14_14
Last ObjectModification: 2018_09_26-AM-10_41_50

Theory : core_2

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