Nuprl Lemma : not_functionality_wrt_iff

[P,Q:ℙ].  ⇐⇒ ¬Q} supposing ⇐⇒ Q


Proof




Definitions occuring in Statement :  uimplies: supposing a uall: [x:A]. B[x] prop: guard: {T} iff: ⇐⇒ Q not: ¬A
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a iff: ⇐⇒ Q and: P ∧ Q implies:  Q not: ¬A false: False prop: rev_implies:  Q
Lemmas referenced :  not_wf iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  introduction cut sqequalHypSubstitution productElimination thin independent_pairFormation lambdaFormation hypothesisEquality hypothesis independent_functionElimination voidElimination extract_by_obid isectElimination independent_pairEquality lambdaEquality dependent_functionElimination because_Cache Error :productIsType,  Error :functionIsType,  Error :universeIsType,  isect_memberEquality equalityTransitivity equalitySymmetry Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[P,Q:\mBbbP{}].    \{\mneg{}P  \mLeftarrow{}{}\mRightarrow{}  \mneg{}Q\}  supposing  P  \mLeftarrow{}{}\mRightarrow{}  Q



Date html generated: 2019_06_20-AM-11_17_05
Last ObjectModification: 2018_09_26-AM-10_24_37

Theory : core_2


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