Nuprl Lemma : div_one
∀[x:ℤ]. (x ÷ 1 ~ x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
divide: n ÷ m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
absval: |i|,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
le: A ≤ B,
subtype_rel: A ⊆r B,
nat: ℕ,
uiff: uiff(P;Q)
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
istype-int,
nequal_wf,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
itermMultiply_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-false,
istype-le,
istype-less_than,
absval_wf,
intformand_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
div_unique3
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
independent_functionElimination,
axiomSqEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
lambdaFormation_alt,
voidElimination,
equalityIstype,
inhabitedIsType,
baseClosed,
sqequalBase,
universeIsType,
dependent_pairFormation_alt,
sqequalRule,
independent_pairFormation,
minusEquality,
because_Cache,
imageMemberEquality,
unionElimination,
approximateComputation,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
imageElimination,
productElimination,
productIsType,
applyEquality,
setElimination,
rename,
baseApply,
closedConclusion,
functionIsType
Latex:
\mforall{}[x:\mBbbZ{}]. (x \mdiv{} 1 \msim{} x)
Date html generated:
2020_05_19-PM-09_41_18
Last ObjectModification:
2019_10_16-PM-04_23_57
Theory : int_2
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