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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