Nuprl Lemma : extend_perm_over_id
∀n:ℕ. (↑{n}(id_perm()) = id_perm() ∈ Sym(n + 1))
Proof
Definitions occuring in Statement :
extend_perm: ↑{n}(p),
sym_grp: Sym(n),
id_perm: id_perm(),
nat: ℕ,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
sym_grp: Sym(n),
perm: Perm(T),
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
id_perm: id_perm(),
extend_perm: ↑{n}(p),
true: True,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
perm_b: p.b,
pi2: snd(t),
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
nat_wf,
inv_funs_wf,
int_seg_wf,
perm_f_wf,
perm_b_wf,
perm_sig_wf,
mk_perm_wf,
identity_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
extend_permf_over_id,
subtype_rel_self,
iff_weakening_equal,
id_perm_wf,
perm_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
dependent_set_memberEquality_alt,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
equalitySymmetry,
sqequalRule,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
inhabitedIsType,
universeEquality,
functionIsType,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. (\muparrow{}\{n\}(id\_perm()) = id\_perm())
Date html generated:
2019_10_16-PM-00_59_59
Last ObjectModification:
2018_10_08-AM-09_14_23
Theory : perms_1
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