Nuprl Lemma : bool-decider_wf
∀[b:𝔹]. (bool-decider(b) ∈ Dec(↑b))
Proof
Definitions occuring in Statement :
bool-decider: bool-decider(b),
assert: ↑b,
bool: 𝔹,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
bool-decider: bool-decider(b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
decidable__assert,
subtype_rel_self,
bool_wf,
decidable_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
functionEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[b:\mBbbB{}]. (bool-decider(b) \mmember{} Dec(\muparrow{}b))
Date html generated:
2018_05_21-PM-06_28_58
Last ObjectModification:
2018_05_19-PM-04_40_06
Theory : general
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