Nuprl Lemma : assert_of_bor
∀p:𝔹. ∀[q:𝔹]. uiff(↑(p ∨bq);(↑p) ∨ (↑q))
Proof
Definitions occuring in Statement :
bor: p ∨bq,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
member: t ∈ T,
it: ⋅,
btrue: tt,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
assert: ↑b,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
or: P ∨ Q,
prop: ℙ,
bfalse: ff,
implies: P ⇒ Q,
guard: {T},
false: False
Lemmas referenced :
assert_wf,
true_wf,
or_wf,
assert_witness,
false_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
sqequalRule,
isect_memberFormation,
independent_pairFormation,
cut,
introduction,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
rename,
inlFormation,
natural_numberEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
independent_functionElimination,
inrFormation,
voidElimination
Latex:
\mforall{}p:\mBbbB{}. \mforall{}[q:\mBbbB{}]. uiff(\muparrow{}(p \mvee{}\msubb{}q);(\muparrow{}p) \mvee{} (\muparrow{}q))
Date html generated:
2016_05_13-PM-03_57_05
Last ObjectModification:
2015_12_26-AM-10_51_47
Theory : bool_1
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