Nuprl Lemma : l_mul_permute
∀[L1,L2:ℤ List]. l_mul(L1) = l_mul(L2) ∈ ℤ supposing permutation(ℤ;L1;L2)
Proof
Definitions occuring in Statement :
l_mul: l_mul(L),
permutation: permutation(T;L1;L2),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_mul: l_mul(L),
assoc: Assoc(T;op),
so_apply: x[s1;s2],
infix_ap: x f y,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
comm: Comm(T;op)
Lemmas referenced :
list_wf,
permutation_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermMultiply_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
reduce-permutation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
multiplyEquality,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
because_Cache,
hypothesis,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L1,L2:\mBbbZ{} List]. l\_mul(L1) = l\_mul(L2) supposing permutation(\mBbbZ{};L1;L2)
Date html generated:
2016_05_14-PM-02_54_26
Last ObjectModification:
2016_01_15-AM-07_29_05
Theory : list_1
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