Nuprl Lemma : zero_sym_grp
∀p:Sym(0). (p = id_perm() ∈ Sym(0))
Proof
Definitions occuring in Statement :
sym_grp: Sym(n),
id_perm: id_perm(),
all: ∀x:A. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
sym_grp: Sym(n),
uall: ∀[x:A]. B[x],
perm: Perm(T),
prop: ℙ,
perm_sig: perm_sig(T),
id_perm: id_perm(),
mk_perm: mk_perm(f;b),
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
subtype_rel: A ⊆r B,
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,
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
lelt_wf,
decidable__equal_int,
int_seg_properties,
perm_b_wf,
perm_f_wf,
inv_funs_wf,
perm_properties,
int_seg_wf,
perm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
dependent_pairEquality,
functionExtensionality,
because_Cache,
applyEquality,
independent_pairFormation,
sqequalRule,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
unionElimination,
functionEquality
Latex:
\mforall{}p:Sym(0). (p = id\_perm())
Date html generated:
2016_05_16-AM-07_32_10
Last ObjectModification:
2016_01_16-PM-10_06_31
Theory : perms_1
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