Nuprl Lemma : ppcc-problem
ff = tt supposing (inl tt) = (inl ff) ∈ (𝔹?)
Proof
Definitions occuring in Statement :
bfalse: ff,
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
unit: Unit,
inl: inl x,
union: left + right,
equal: s = t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
outl: outl(x),
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
btrue_wf,
bfalse_wf,
and_wf,
equal_wf,
bool_wf,
unit_wf2,
outl_wf,
assert_wf,
isl_wf,
btrue_neq_bfalse,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
hypothesis,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
equalityTransitivity,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
independent_isectElimination,
hyp_replacement,
Error :applyLambdaEquality,
natural_numberEquality,
setEquality,
independent_functionElimination,
voidElimination,
baseClosed
Latex:
ff = tt supposing (inl tt) = (inl ff)
Date html generated:
2016_10_25-AM-10_43_49
Last ObjectModification:
2016_07_12-AM-06_54_15
Theory : general
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