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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