Nuprl Lemma : map-decide
∀[b,f,L1,L2:Top].
(map(f;case b of inl(a) => L1[a] | inr(a) => L2[a]) ~ case b of inl(a) => map(f;L1[a]) | inr(a) => map(f;L2[a]))
Proof
Definitions occuring in Statement :
map: map(f;as),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
map: map(f;as),
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
so_apply: x[s],
uall: ∀[x:A]. B[x],
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],
top: Top,
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 :
top_wf,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-decide
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
introduction,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
because_Cache,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[b,f,L1,L2:Top].
(map(f;case b of inl(a) => L1[a] | inr(a) => L2[a]) \msim{} case b
of inl(a) =>
map(f;L1[a])
| inr(a) =>
map(f;L2[a]))
Date html generated:
2016_05_15-PM-04_33_16
Last ObjectModification:
2016_01_16-AM-11_16_26
Theory : general
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