Nuprl Lemma : eq_bool_wf
∀[p,q:𝔹]. (p =b q ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq_bool: p =b q,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eq_bool: p =b q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
bor_wf,
band_wf,
assert_wf,
bnot_wf,
assert_of_bnot,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
hypothesis,
productElimination,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :universeIsType
Latex:
\mforall{}[p,q:\mBbbB{}]. (p =b q \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_31_11
Last ObjectModification:
2018_09_26-AM-11_24_47
Theory : bool_1
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