Nuprl Lemma : not-isr-isl
∀x:Top + Top. ((¬↑isr(x)) ⇒ (isl(x) ~ tt))
Proof
Definitions occuring in Statement :
assert: ↑b,
isr: isr(x),
isl: isl(x),
btrue: tt,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
union: left + right,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
isr: isr(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
isl: isl(x),
btrue: tt,
not: ¬A,
true: True,
false: False,
sq_type: SQType(T),
guard: {T},
prop: ℙ
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
btrue_wf,
not_wf,
assert_wf,
isr_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
unionElimination,
sqequalRule,
independent_functionElimination,
natural_numberEquality,
voidElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
unionEquality
Latex:
\mforall{}x:Top + Top. ((\mneg{}\muparrow{}isr(x)) {}\mRightarrow{} (isl(x) \msim{} tt))
Date html generated:
2016_05_13-PM-03_20_26
Last ObjectModification:
2015_12_26-AM-09_10_52
Theory : union
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