Nuprl Lemma : test-omega
∀x,y,z:ℤ. ((1 ≤ ((2 * x) + (2 * y))) ⇒ ((2 * x) ≤ ((2 * y) + 1)) ⇒ (2 ≤ (3 * y)))
Proof
Definitions occuring in Statement :
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
natural_numberEquality,
multiplyEquality,
hypothesisEquality,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
addEquality
Latex:
\mforall{}x,y,z:\mBbbZ{}. ((1 \mleq{} ((2 * x) + (2 * y))) {}\mRightarrow{} ((2 * x) \mleq{} ((2 * y) + 1)) {}\mRightarrow{} (2 \mleq{} (3 * y)))
Date html generated:
2017_09_29-PM-05_56_30
Last ObjectModification:
2017_06_01-PM-01_27_20
Theory : omega
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