### Nuprl Lemma : proof-by-cont-implies-LEM

`(∀p:ℙ. ((¬¬p) `` p)) `` (∀p:ℙ. (p ∨ (¬p)))`

Proof

Definitions occuring in Statement :  prop: `ℙ` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` or: `P ∨ Q`
Definitions unfolded in proof :  implies: `P `` Q` all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` not: `¬A` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` false: `False` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  or_wf not_wf not_over_or all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut hypothesis sqequalHypSubstitution dependent_functionElimination thin lemma_by_obid isectElimination hypothesisEquality independent_functionElimination productElimination independent_isectElimination voidElimination universeEquality instantiate sqequalRule lambdaEquality cumulativity functionEquality

Latex:
(\mforall{}p:\mBbbP{}.  ((\mneg{}\mneg{}p)  {}\mRightarrow{}  p))  {}\mRightarrow{}  (\mforall{}p:\mBbbP{}.  (p  \mvee{}  (\mneg{}p)))

Date html generated: 2016_05_13-PM-03_46_05
Last ObjectModification: 2015_12_26-AM-09_58_41

Theory : call!by!value_2

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