Nuprl Lemma : int_nzero-rational
∀[z:ℤ-o]. (¬(z = 0 ∈ ℚ))
Proof
Definitions occuring in Statement :
rationals: ℚ,
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_nzero_wf,
not_wf,
int-subtype-rationals,
nequal_wf,
subtype_rel_set,
rationals_wf,
equal-wf-T-base,
int-equal-in-rationals,
equal_wf,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_nzero_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
intEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
addLevel,
impliesFunctionality,
productElimination,
applyEquality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[z:\mBbbZ{}\msupminus{}\msupzero{}]. (\mneg{}(z = 0))
Date html generated:
2016_05_15-PM-11_33_36
Last ObjectModification:
2016_01_16-PM-09_13_08
Theory : rationals
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