### Nuprl Lemma : list_accum-map

`∀[L,y,f,g:Top].`
`  (accumulate (with value x and list item a):`
`    f[x;a]`
`   over list:`
`     map(g;L)`
`   with starting value:`
`    y) ~ accumulate (with value x and list item a):`
`          f[x;g a]`
`         over list:`
`           L`
`         with starting value:`
`          y))`

Proof

Definitions occuring in Statement :  map: `map(f;as)` list_accum: list_accum uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s1;s2]` apply: `f a` sqequal: `s ~ t`
Definitions unfolded in proof :  map: `map(f;as)` uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` list_ind: list_ind nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` list_accum: list_accum so_apply: `x[s1;s2]` fun_exp: `f^n` primrec: `primrec(n;b;c)` top: `Top` so_lambda: `λ2x.t[x]` so_apply: `x[s]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` uiff: `uiff(P;Q)` subtract: `n - m` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` nat_plus: `ℕ+` so_lambda: `so_lambda(x,y,z,w.t[x; y; z; w])` so_apply: `x[s1;s2;s3;s4]` strict4: `strict4(F)` has-value: `(a)↓` squash: `↓T` cons: `[a / b]` so_lambda: `λ2x y.t[x; y]` nil: `[]` it: `⋅`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  introduction cut thin sqequalSqle lambdaFormation fixpointLeast extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination axiomSqleEquality isect_memberEquality voidEquality unionElimination independent_pairFormation productElimination addEquality applyEquality intEquality minusEquality because_Cache dependent_set_memberEquality baseClosed callbyvalueCallbyvalue callbyvalueReduce baseApply closedConclusion callbyvalueExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqleReflexivity divergentSqle axiomSqEquality

Latex:
\mforall{}[L,y,f,g:Top].
(accumulate  (with  value  x  and  list  item  a):
f[x;a]
over  list:
map(g;L)
with  starting  value:
y)  \msim{}  accumulate  (with  value  x  and  list  item  a):
f[x;g  a]
over  list:
L
with  starting  value:
y))

Date html generated: 2019_06_20-PM-00_39_06
Last ObjectModification: 2018_09_26-PM-02_46_56

Theory : list_0

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