Nuprl Lemma : band_ff_simp
∀[u:𝔹]. u ∧b ff = ff
Proof
Definitions occuring in Statement :
band: p ∧b q,
bfalse: ff,
bool: 𝔹,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
band: p ∧b q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
bfalse_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :universeIsType,
Error :isect_memberFormation_alt,
sqequalRule,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination
Latex:
\mforall{}[u:\mBbbB{}]. u \mwedge{}\msubb{} ff = ff
Date html generated:
2019_06_20-AM-11_31_02
Last ObjectModification:
2018_09_26-AM-11_13_39
Theory : bool_1
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