Nuprl Lemma : nat_add_mon_wf
<ℕ,+> ∈ GrpSig
Proof
Definitions occuring in Statement :
nat_add_mon: <ℕ,+>,
grp_sig: GrpSig,
member: t ∈ T
Definitions unfolded in proof :
nat_add_mon: <ℕ,+>,
grp_sig: GrpSig,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
bool_wf,
false_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
le_int_wf,
eq_int_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairEquality,
cut,
lemma_by_obid,
hypothesis,
lambdaEquality,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
because_Cache,
dependent_set_memberEquality,
addEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
lambdaFormation,
functionEquality,
productEquality,
cumulativity
Latex:
<\mBbbN{},+> \mmember{} GrpSig
Date html generated:
2016_05_15-PM-00_17_50
Last ObjectModification:
2016_01_15-PM-11_05_52
Theory : groups_1
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