Nuprl Lemma : bor_wf
∀[p,q:𝔹]. (p ∨bq ∈ 𝔹)
Proof
Definitions occuring in Statement :
bor: p ∨bq,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bor: p ∨bq,
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,
prop: ℙ
Lemmas referenced :
bool_wf,
eqtt_to_assert,
btrue_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesisEquality,
thin,
extract_by_obid,
hypothesis,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
baseClosed,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType
Latex:
\mforall{}[p,q:\mBbbB{}]. (p \mvee{}\msubb{}q \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_30_59
Last ObjectModification:
2018_09_26-AM-11_13_39
Theory : bool_1
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