Nuprl Lemma : decidable__equal_bool
∀a,b:𝔹. Dec(a = b)
Proof
Definitions occuring in Statement :
bool: 𝔹,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
decidable: Dec(P),
bool: 𝔹,
unit: Unit,
member: t ∈ T,
it: ⋅,
btrue: tt,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
bfalse: ff,
guard: {T},
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
btrue_wf,
not_wf,
equal-wf-base,
bool_wf,
btrue_neq_bfalse,
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,
sqequalRule,
baseClosed,
because_Cache,
Error :inrFormation_alt,
equalitySymmetry,
independent_functionElimination,
voidElimination,
Error :equalityIsType4,
Error :inhabitedIsType,
hypothesisEquality
Latex:
\mforall{}a,b:\mBbbB{}. Dec(a = b)
Date html generated:
2019_06_20-AM-11_31_19
Last ObjectModification:
2018_09_28-PM-11_33_56
Theory : bool_1
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