Nuprl Lemma : band_wf
∀[p,q:𝔹]. (p ∧b q ∈ 𝔹)
Proof
Definitions occuring in Statement :
band: 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,
band: p ∧b q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesisEquality,
Error :inhabitedIsType,
hypothesis,
Error :lambdaFormation_alt,
thin,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
extract_by_obid,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
baseClosed,
independent_functionElimination,
Error :equalityIsType1,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
Error :isect_memberEquality_alt,
Error :universeIsType
Latex:
\mforall{}[p,q:\mBbbB{}]. (p \mwedge{}\msubb{} q \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_30_58
Last ObjectModification:
2018_10_06-AM-10_10_35
Theory : bool_1
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