Nuprl Lemma : bool_sim_false
∀[b:𝔹]. b ~ ff supposing b = ff
Proof
Definitions occuring in Statement : 
bfalse: ff
, 
bool: 𝔹
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
sqequal: s ~ t
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
prop: ℙ
Lemmas referenced : 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
equal_wf, 
bfalse_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
hypothesis, 
independent_isectElimination, 
dependent_functionElimination, 
hypothesisEquality, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
sqequalAxiom, 
sqequalRule, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[b:\mBbbB{}].  b  \msim{}  ff  supposing  b  =  ff
Date html generated:
2016_05_13-PM-03_55_25
Last ObjectModification:
2015_12_26-AM-10_53_12
Theory : bool_1
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