Nuprl Lemma : posint_cancel
Cancel(|<ℤ+,*>|;|<ℤ+,*>|;*)
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
grp_op: *,
grp_car: |g|,
cancel: Cancel(T;S;op)
Definitions unfolded in proof :
cancel: Cancel(T;S;op),
posint_mul_mon: <ℤ+,*>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
set_subtype_base,
less_than_wf,
istype-int,
int_subtype_base,
nat_plus_wf,
mul_cancel_in_eq,
nat_plus_inc_int_nzero,
nat_plus_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
equalityIsType4,
inhabitedIsType,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
independent_isectElimination,
isect_memberEquality_alt,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeIsType,
setElimination,
rename,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
voidElimination,
independent_pairFormation,
dependent_set_memberEquality_alt
Latex:
Cancel(|<\mBbbZ{}\msupplus{},*>|;|<\mBbbZ{}\msupplus{},*>|;*)
Date html generated:
2019_10_16-PM-01_06_00
Last ObjectModification:
2018_10_08-PM-00_36_48
Theory : factor_1
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