Nuprl Lemma : trivial_sym_grp
∀p:Sym(1). (p = id_perm() ∈ Sym(1))
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,
id_perm: id_perm(),
perm_sig: perm_sig(T),
mk_perm: mk_perm(f;b)
Lemmas referenced :
perm_wf,
int_seg_wf,
perm_properties,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
trivial_nat1_fun
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
productElimination,
dependent_pairEquality_alt,
inhabitedIsType
Latex:
\mforall{}p:Sym(1). (p = id\_perm())
Date html generated:
2019_10_16-PM-01_00_16
Last ObjectModification:
2018_10_08-AM-09_08_23
Theory : perms_1
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