Nuprl Lemma : bimplies_wf
∀[p:𝔹]. ∀[q:𝔹 supposing ↑p]. (p ⇒b q ∈ 𝔹)
Proof
Definitions occuring in Statement :
bimplies: p ⇒b q,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bimplies: p ⇒b q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
bor: p ∨bq,
bfalse: ff,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
true: True,
istype: istype(T)
Lemmas referenced :
isect_subtype_rel_trivial,
true_wf,
bool_wf,
btrue_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
sqequalRule,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
hypothesis,
because_Cache,
Error :lambdaEquality_alt,
Error :universeIsType,
independent_isectElimination,
independent_pairFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isectIsType,
Error :inhabitedIsType,
Error :isect_memberEquality_alt
Latex:
\mforall{}[p:\mBbbB{}]. \mforall{}[q:\mBbbB{} supposing \muparrow{}p]. (p {}\mRightarrow{}\msubb{} q \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_31_13
Last ObjectModification:
2018_10_08-PM-05_04_03
Theory : bool_1
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