Nuprl Lemma : band-simple-int_eq
∀[a,b,c:Top]. (if a=b then inl ⋅ else (inr ⋅ ) ∧b c ~ if a=b then c else (inr ⋅ ))
Proof
Definitions occuring in Statement :
band: p ∧b q,
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
int_eq: if a=b then c else d,
inr: inr x ,
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
it: ⋅,
band: p ∧b q,
uall: ∀[x:A]. B[x],
bfalse: ff,
ifthenelse: if b then t else f fi ,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T
Lemmas referenced :
lifting-strict-int_eq,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesis,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
isect_memberFormation,
sqequalAxiom,
isectEquality
Latex:
\mforall{}[a,b,c:Top]. (if a=b then inl \mcdot{} else (inr \mcdot{} ) \mwedge{}\msubb{} c \msim{} if a=b then c else (inr \mcdot{} ))
Date html generated:
2017_10_01-AM-08_39_28
Last ObjectModification:
2017_07_26-PM-04_27_31
Theory : untyped!computation
Home
Index