Nuprl Lemma : assert_of_bimplies
∀[p:𝔹]. ∀[q:𝔹 supposing ↑p]. uiff(↑(p ⇒b q);↑q supposing ↑p)
Proof
Definitions occuring in Statement :
bimplies: p ⇒b q,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bimplies: p ⇒b q,
bor: p ∨bq,
bnot: ¬bb,
bfalse: ff,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
true: True
Lemmas referenced :
assert_witness,
isect_subtype_rel_trivial,
assert_wf,
bool_wf,
subtype_rel_self,
bimplies_wf,
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
independent_isectElimination,
hypothesis,
unionElimination,
thin,
equalityElimination,
sqequalRule,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
lambdaEquality,
independent_functionElimination,
Error :universeIsType,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
Error :isectIsType,
productElimination,
independent_pairEquality,
Error :inhabitedIsType,
isectEquality
Latex:
\mforall{}[p:\mBbbB{}]. \mforall{}[q:\mBbbB{} supposing \muparrow{}p]. uiff(\muparrow{}(p {}\mRightarrow{}\msubb{} q);\muparrow{}q supposing \muparrow{}p)
Date html generated:
2019_06_20-AM-11_31_37
Last ObjectModification:
2018_09_26-AM-11_24_51
Theory : bool_1
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