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
Home
Index