Nuprl Lemma : iff_imp_equal_bool
∀[a,b:𝔹]. a = b supposing ↑a ⇐⇒ ↑b
Proof
Definitions occuring in Statement :
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
true: True,
bfalse: ff,
ifthenelse: if b then t else f fi ,
assert: ↑b,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹
Lemmas referenced :
assert_wf,
iff_wf,
bool_wf,
bfalse_wf,
btrue_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis,
sqequalRule,
Error :productIsType,
Error :functionIsType,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
voidElimination,
natural_numberEquality,
independent_functionElimination,
productElimination,
equalityElimination,
unionElimination
Latex:
\mforall{}[a,b:\mBbbB{}]. a = b supposing \muparrow{}a \mLeftarrow{}{}\mRightarrow{} \muparrow{}b
Date html generated:
2019_06_20-AM-11_31_25
Last ObjectModification:
2018_09_26-AM-11_16_10
Theory : bool_1
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