Nuprl Lemma : nat-pred_wf
∀[n:ℕ]. (n-1 ∈ ℕ)
Proof
Definitions occuring in Statement :
nat-pred: n-1,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
nat-pred: n-1,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
subtract_wf,
le_wf,
false_wf
Rules used in proof :
axiomEquality,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
hypothesisEquality,
isectElimination,
extract_by_obid,
lambdaFormation,
independent_pairFormation,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
natural_numberEquality,
hypothesis,
because_Cache,
rename,
thin,
setElimination,
sqequalHypSubstitution,
int_eqEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. (n-1 \mmember{} \mBbbN{})
Date html generated:
2017_04_21-AM-11_21_13
Last ObjectModification:
2017_04_20-PM-03_36_24
Theory : continuity
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