Nuprl Lemma : band_ff
∀[u:𝔹]. (u ∧b ff ~ ff)
Proof
Definitions occuring in Statement :
band: p ∧b q,
bfalse: ff,
bool: 𝔹,
uall: ∀[x:A]. B[x],
sqequal: s ~ 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 :
bool_wf
Rules used in proof :
sqequalReflexivity,
universeIsType,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
hypothesis,
isect_memberFormation_alt,
sqequalRule,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
axiomSqEquality
Latex:
\mforall{}[u:\mBbbB{}]. (u \mwedge{}\msubb{} ff \msim{} ff)
Date html generated:
2020_05_19-PM-09_36_01
Last ObjectModification:
2020_02_17-PM-00_40_33
Theory : bool_1
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