Nuprl Lemma : name_eq-normalize2
∀[F,G,X,a,b:Top].
(case name_eq(a;b) ∧b X of inl(x) => F a | inr(y) => G ~ case name_eq(a;b) ∧b X of inl(x) => F b | inr(y) => G)
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
band: p ∧b q,
bfalse: ff,
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
ifthenelse: if b then t else f fi ,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
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 :
name_eq-normalize,
lifting-strict-decide,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
sqequalRule,
baseClosed,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesis,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[F,G,X,a,b:Top].
(case name\_eq(a;b) \mwedge{}\msubb{} X of inl(x) => F a | inr(y) => G \msim{} case name\_eq(a;b) \mwedge{}\msubb{} X
of inl(x) =>
F b
| inr(y) =>
G)
Date html generated:
2017_04_17-AM-09_17_32
Last ObjectModification:
2017_02_27-PM-05_21_48
Theory : decidable!equality
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