Nuprl Lemma : divides_anti_sym_n
∀[a,b:ℕ]. (a = b ∈ ℤ) supposing ((b | a) and (a | b))
Proof
Definitions occuring in Statement :
divides: b | a,
nat: ℕ,
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,
prop: ℙ,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
divides: b | a,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
nat_plus: ℕ+,
le: A ≤ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
less_than': less_than'(a;b),
true: True,
subtract: n - m
Lemmas referenced :
divides_wf,
nat_wf,
decidable__equal_int,
equal-wf-T-base,
int_subtype_base,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
itermMultiply_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf,
divisors_bound,
decidable__lt,
false_wf,
not-lt-2,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
less_than_wf,
intformle_wf,
int_formula_prop_le_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
productElimination,
hyp_replacement,
Error :applyLambdaEquality,
intEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
lambdaFormation,
independent_functionElimination,
addEquality,
minusEquality
Latex:
\mforall{}[a,b:\mBbbN{}]. (a = b) supposing ((b | a) and (a | b))
Date html generated:
2016_10_21-AM-11_07_37
Last ObjectModification:
2016_07_12-AM-06_00_22
Theory : num_thy_1
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