Nuprl Lemma : extend_perm_over_comp
∀n:ℕ. ∀p,q:Sym(n). (↑{n}(p O q) = ↑{n}(p) O ↑{n}(q) ∈ Sym(n + 1))
Proof
Definitions occuring in Statement :
extend_perm: ↑{n}(p),
sym_grp: Sym(n),
comp_perm: comp_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),
uall: ∀[x:A]. B[x],
nat: ℕ,
perm: Perm(T),
prop: ℙ,
extend_perm: ↑{n}(p),
comp_perm: comp_perm,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
perm_b: p.b,
pi2: snd(t),
true: True,
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 :
perm_wf,
int_seg_wf,
nat_wf,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
perm_properties,
perm_sig_wf,
mk_perm_wf,
compose_wf,
extend_permf_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
extend_permf_over_comp,
subtype_rel_self,
iff_weakening_equal,
extend_perm_wf,
comp_perm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
inhabitedIsType,
hypothesisEquality,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
addEquality,
because_Cache,
sqequalRule,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionIsType,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p,q:Sym(n). (\muparrow{}\{n\}(p O q) = \muparrow{}\{n\}(p) O \muparrow{}\{n\}(q))
Date html generated:
2019_10_16-PM-01_00_02
Last ObjectModification:
2018_10_08-AM-09_12_47
Theory : perms_1
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