Nuprl Lemma : Peirce's-law-iff-xmiddle
∀[P,B:ℙ]. (((P ⇒ B) ⇒ P) ⇒ P) ⇐⇒ ∀[P,B:ℙ]. (P ∨ (P ⇒ B))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
or: P ∨ Q,
guard: {T}
Lemmas referenced :
uall_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation,
isect_memberFormation,
universeEquality,
cut,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
cumulativity,
functionEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
inrFormation,
inlFormation,
because_Cache,
unionElimination
Latex:
\mforall{}[P,B:\mBbbP{}]. (((P {}\mRightarrow{} B) {}\mRightarrow{} P) {}\mRightarrow{} P) \mLeftarrow{}{}\mRightarrow{} \mforall{}[P,B:\mBbbP{}]. (P \mvee{} (P {}\mRightarrow{} B))
Date html generated:
2016_05_15-PM-03_19_03
Last ObjectModification:
2015_12_27-PM-01_03_37
Theory : general
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