Nuprl Lemma : not-isl-assert-isr
∀x:Top + Top. ((¬↑isl(x)) ⇒ (↑isr(x)))
Proof
Definitions occuring in Statement :
assert: ↑b,
isr: isr(x),
isl: isl(x),
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
union: left + right
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
not-isl-isr,
not_wf,
assert_wf,
isl_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
natural_numberEquality,
isectElimination,
unionEquality
Latex:
\mforall{}x:Top + Top. ((\mneg{}\muparrow{}isl(x)) {}\mRightarrow{} (\muparrow{}isr(x)))
Date html generated:
2016_05_13-PM-03_20_29
Last ObjectModification:
2015_12_26-AM-09_10_50
Theory : union
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