Nuprl Lemma : bool_cases
∀b:𝔹. (b = tt ∨ b = ff)
Proof
Definitions occuring in Statement :
bfalse: ff,
btrue: tt,
bool: 𝔹,
all: ∀x:A. B[x],
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
member: t ∈ T,
it: ⋅,
btrue: tt,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
bfalse: ff
Lemmas referenced :
btrue_wf,
equal-wf-base,
bool_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
Error :inlFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :universeIsType,
isectElimination,
baseClosed,
Error :inrFormation_alt,
because_Cache
Latex:
\mforall{}b:\mBbbB{}. (b = tt \mvee{} b = ff)
Date html generated:
2019_06_20-AM-11_19_51
Last ObjectModification:
2018_09_27-PM-06_23_29
Theory : basic_types
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