### Nuprl Lemma : callbyvalueall_seq-combine2-0

`∀[F,L1,L2:Top]. ∀[m1,m2:ℕ].`
`  (callbyvalueall_seq(L1;λx.x;λg.callbyvalueall_seq(L2[g];λx.x;F;0;m2);0;m1) `
`  ~ callbyvalueall_seq(λi.if i <z m1 then L1 i else mk_lambdas_fun(λg.(L2[g] (i - m1));m1) fi ;λx.x`
`                      ;λg.(F partial_ap_gen(g;m1 + m2;m1;m2));0;m1 + m2))`

Proof

Definitions occuring in Statement :  partial_ap_gen: `partial_ap_gen(g;n;s;m)` mk_lambdas_fun: `mk_lambdas_fun(F;m)` callbyvalueall_seq: `callbyvalueall_seq(L;G;F;n;m)` nat: `ℕ` ifthenelse: `if b then t else f fi ` lt_int: `i <z j` uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` apply: `f a` lambda: `λx.A[x]` subtract: `n - m` add: `n + m` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` top: `Top` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` nat: `ℕ` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` mk_applies: `mk_applies(F;G;m)`
Lemmas referenced :  top_wf nat_wf primrec0_lemma lelt_wf int_formula_prop_wf int_formula_prop_le_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformle_wf itermVar_wf itermAdd_wf itermConstant_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt nat_properties false_wf callbyvalueall_seq-combine2
Rules used in proof :  cut lemma_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesisEquality isect_memberEquality voidElimination voidEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation sqequalRule lambdaFormation hypothesis setElimination rename dependent_functionElimination addEquality unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality computeAll because_Cache isect_memberFormation introduction sqequalAxiom

Latex:
\mforall{}[F,L1,L2:Top].  \mforall{}[m1,m2:\mBbbN{}].
(callbyvalueall\_seq(L1;\mlambda{}x.x;\mlambda{}g.callbyvalueall\_seq(L2[g];\mlambda{}x.x;F;0;m2);0;m1)
\msim{}  callbyvalueall\_seq(\mlambda{}i.if  i  <z  m1  then  L1  i  else  mk\_lambdas\_fun(\mlambda{}g.(L2[g]  (i  -  m1));m1)  fi  ;\mlambda{}x.x
;\mlambda{}g.(F  partial\_ap\_gen(g;m1  +  m2;m1;m2));0;m1  +  m2))

Date html generated: 2016_05_15-PM-02_14_29
Last ObjectModification: 2016_01_15-PM-10_17_45

Theory : untyped!computation

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