Nuprl Lemma : sqequal-ff-to-assert
∀[t:𝔹]. uiff(t ~ ff;¬↑t)
Proof
Definitions occuring in Statement :
assert: ↑b
,
bfalse: ff
,
bool: 𝔹
,
uiff: uiff(P;Q)
,
uall: ∀[x:A]. B[x]
,
not: ¬A
,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
not: ¬A
,
implies: P
⇒ Q
,
false: False
,
assert: ↑b
,
ifthenelse: if b then t else f fi
,
bfalse: ff
,
prop: ℙ
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
sq_type: SQType(T)
,
all: ∀x:A. B[x]
,
guard: {T}
Lemmas referenced :
false_wf,
assert_wf,
bool_sq,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
bfalse_wf,
not_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
voidElimination,
lemma_by_obid,
independent_functionElimination,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
sqequalIntensionalEquality,
instantiate,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom,
productElimination,
independent_pairEquality,
isect_memberEquality
Latex:
\mforall{}[t:\mBbbB{}]. uiff(t \msim{} ff;\mneg{}\muparrow{}t)
Date html generated:
2016_05_15-PM-03_14_32
Last ObjectModification:
2015_12_27-PM-01_02_16
Theory : general
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