Nuprl Lemma : list_accum_pair_wf
∀[T,A,B:Type]. ∀[a0:A]. ∀[b0:B]. ∀[f:A ⟶ T ⟶ A]. ∀[g:B ⟶ T ⟶ B]. ∀[L:T List].
(list_accum_pair(a,x.f[a;x];b,x.g[b;x];a0;b0;L) ∈ A × B)
Proof
Definitions occuring in Statement :
list_accum_pair: list_accum_pair(a,x.f[a; x];b,x.g[b; x];a0;b0;L),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_accum_pair: list_accum_pair(a,x.f[a; x];b,x.g[b; x];a0;b0;L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productEquality,
independent_pairEquality,
lambdaEquality,
spreadEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T,A,B:Type]. \mforall{}[a0:A]. \mforall{}[b0:B]. \mforall{}[f:A {}\mrightarrow{} T {}\mrightarrow{} A]. \mforall{}[g:B {}\mrightarrow{} T {}\mrightarrow{} B]. \mforall{}[L:T List].
(list\_accum\_pair(a,x.f[a;x];b,x.g[b;x];a0;b0;L) \mmember{} A \mtimes{} B)
Date html generated:
2016_05_15-PM-03_47_46
Last ObjectModification:
2015_12_27-PM-01_21_26
Theory : general
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