Nuprl Lemma : not-not-assert
∀[b:𝔹]. uiff(¬¬↑b;↑b)
Proof
Definitions occuring in Statement :
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
not: ¬A,
false: False,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
assert_witness,
not_wf,
assert_wf,
false_wf,
bool_wf,
decidable__assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
lambdaFormation,
lambdaEquality,
voidElimination,
functionEquality,
sqequalRule,
dependent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
unionElimination
Latex:
\mforall{}[b:\mBbbB{}]. uiff(\mneg{}\mneg{}\muparrow{}b;\muparrow{}b)
Date html generated:
2016_05_15-PM-03_27_14
Last ObjectModification:
2015_12_27-PM-01_08_22
Theory : general
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