Nuprl Lemma : uimplies_antisymmetry
∀[P,Q:ℙ]. (Q supposing P ⇒ P supposing Q ⇒ uiff(P;Q))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
hypothesisEquality,
lambdaEquality,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (Q supposing P {}\mRightarrow{} P supposing Q {}\mRightarrow{} uiff(P;Q))
Date html generated:
2016_05_13-PM-03_07_45
Last ObjectModification:
2016_01_06-PM-05_28_09
Theory : core_2
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