Nuprl Lemma : trivial-int-eq1
∀[x,y:ℤ]. (((x - y) + y ~ x) ∧ (y + (x - y) ~ x) ∧ ((x + y) - y ~ x) ∧ (y - y - x ~ x))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
and: P ∧ Q,
subtract: n - m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
top: Top,
uimplies: b supposing a,
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,
prop: ℙ,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
int_subtype_base,
subtype_base_sq,
add-subtract-cancel,
add-commutes,
subtract-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
sqequalRule,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
instantiate,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productElimination,
independent_pairEquality,
sqequalAxiom
Latex:
\mforall{}[x,y:\mBbbZ{}]. (((x - y) + y \msim{} x) \mwedge{} (y + (x - y) \msim{} x) \mwedge{} ((x + y) - y \msim{} x) \mwedge{} (y - y - x \msim{} x))
Date html generated:
2016_05_15-PM-03_23_21
Last ObjectModification:
2016_01_16-AM-10_47_43
Theory : general
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